Generating function for k=6

Generating function for k=6

x⁶ +6 x⁷ +25 x⁸ +99 x⁹ +385 x¹⁰ +1472 x¹¹ +5676 x¹² +22101 x¹³ +87404 x¹⁴ +350097 x¹⁵ + 1.413251 x¹⁶ + 5.708158 x¹⁷ + 22.903161 x¹⁸ + 90.699398 x¹⁹ + 352.749035 x²⁰ + 1342.638839 x²¹ + 4990.325414 x²² + 18090.636016 x²³ + 63933.709870 x²⁴ + 220277.491298 x²⁵ + 740170.023052 x²⁶ + 2.426954.735273 x²⁷ + 7.770739.437179 x²⁸ + 24.314436.451415 x²⁹ + 74.406425.640743 x³⁰ + 222.867051.758565 x³¹ + 653.898059.035166 x³² + 1880.758487.569235 x³³ + 5306.801737.859823 x³⁴ + 14699.896695.743427 x³⁵ + 40000.754073.015892 x³⁶ + 106996.986698.879002 x³⁷ + 281506.073443.313659 x³⁸ + 728898.531960.024394 x³⁹ + 1.858433.921367.866361 x⁴⁰ + 4.668244.891337.583270 x⁴¹ + 11.558487.906882.611007 x⁴² + 28.222344.432999.095724 x⁴³ + 67.986643.854558.389700 x⁴⁴ + 161.650458.785373.597352 x⁴⁵ + 379.514738.886856.368891 x⁴⁶ + 880.128272.497749.579342 x⁴⁷ + 2016.918676.403737.078155 x⁴⁸ + 4568.862138.116766.909958 x⁴⁹ + 10234.114311.135482.257380 x⁵⁰ + 22675.342340.852081.675183 x⁵¹ + 49710.894902.693897.162246 x⁵² + 107862.502394.920020.826392 x⁵³ + 231703.308739.592039.677816 x⁵⁴ + 492893.832763.214517.649748 x⁵⁵ + 1.038593.768643.968937.338952 x⁵⁶ + 2.168285.505115.303614.278561 x⁵⁷ + 4.486096.488301.652205.060998 x⁵⁸ + 9.200280.264997.382726.663149 x⁵⁹ + 18.707204.177409.321631.309348 x⁶⁰ + 37.721029.937667.109310.348239 x⁶¹ + 75.441970.651189.015102.236884 x⁶² + 149.686302.852480.579616.887590 x⁶³ + 294.694668.411193.943302.649591 x⁶⁴ + 575.787653.304692.261801.419533 x⁶⁵ + 1116.678452.091042.736657.441283 x⁶⁶ + 2150.021671.976599.135934.735063 x⁶⁷ + 4110.333916.578481.640015.516450 x⁶⁸ + 7803.674833.686340.531542.646972 x⁶⁹ + 14715.496988.489783.282584.218666 x⁷⁰ + 27565.642776.213139.359584.714168 x⁷¹ + 51302.713827.461383.366915.116205 x⁷² + 94874.865744.999294.675102.642436 x⁷³ + 174364.593239.669675.063340.802114 x⁷⁴ + 318505.951759.391405.303906.130480 x⁷⁵ + 578339.695028.524750.707999.711094 x⁷⁶ + 1.044015.721734.880516.711009.468004 x⁷⁷ + 1.873874.232582.003564.565493.336767 x⁷⁸ + 3.344509.493339.858047.312329.027851 x⁷⁹ + 5.936504.027626.809256.654952.380832 x⁸⁰ + 10.480494.276589.867957.866681.343162 x⁸¹ + 18.404769.701911.543055.914153.204834 x⁸² + 32.152909.822643.515875.484945.277896 x⁸³ + 55.884817.806444.707134.343071.834849 x⁸⁴ + 96.647858.930611.885361.533287.002129 x⁸⁵ + 166.324218.707856.187655.655080.996168 x⁸⁶ + 284.854116.317471.146239.556983.405989 x⁸⁷ + 485.546781.255574.963192.945335.748753 x⁸⁸ + 823.792841.960344.678875.013758.481177 x⁸⁹ + 1391.294560.514411.668857.798538.306280 x⁹⁰ + 2339.209510.988573.961187.119137.985973 x⁹¹ + 3915.633275.786850.521950.581160.358524 x⁹² + 6526.055407.349405.536831.001983.485724 x⁹³ + 10830.474855.793739.925966.355462.095177 x⁹⁴ + 17898.784652.861421.440079.599011.372285 x⁹⁵ + 29458.416251.570992.065931.905611.365434 x⁹⁶ + 48287.506827.811772.258633.296562.503909 x⁹⁷ + 78836.745521.921798.700139.641789.950508 x⁹⁸ + 128209.252363.794136.495801.066079.409123 x⁹⁹ + 207698.988183.898791.850747.479678.373283 x¹⁰⁰

Generating function for k=6