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Expansion of Sum_{n>=1} ( (1 + x^n)^n - 1 ).
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16
1, 2, 3, 5, 5, 9, 7, 14, 10, 20, 11, 31, 13, 35, 25, 45, 17, 74, 19, 70, 56, 77, 23, 161, 26, 104, 111, 154, 29, 261, 31, 222, 198, 170, 56, 536, 37, 209, 325, 496, 41, 623, 43, 605, 626, 299, 47, 1407, 50, 602, 731, 1092, 53, 1305, 517, 1443, 1026, 464, 59, 4002, 61, 527, 1429, 2381, 1352, 2596, 67, 3009, 1840, 2787, 71, 6719, 73, 740, 5378, 4655, 407, 5135, 79, 10118
a(n) = Sum_{d|n} d^(d - n/d) * binomial(d, n/d).
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1, 4, 27, 257, 3125, 46665, 823543, 16777312, 387420490, 10000001250, 285311670611, 8916100467712, 302875106592253, 11112006825910963, 437893890380859625, 18446744073716891649, 827240261886336764177, 39346408075296709766628, 1978419655660313589123979
Expansion of Sum_{n>=1} ( (3 + x^n)^n - 3^n ).
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5
1, 6, 27, 109, 405, 1467, 5103, 17550, 59050, 197100, 649539, 2126991, 6908733, 22325625, 71744625, 229602925, 731794257, 2324602206, 7360989291, 23245524600, 73222475256, 230128853031, 721764371007, 2259440202825, 7060738412026, 22029517662984, 68630377426119, 213516777941712, 663426981193869, 2058911488612863, 6382625094934119, 19765549255048254, 61149666233193318
a(n) = Sum_{d|n} d^d * binomial(d, n/d).
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1, 8, 81, 1028, 15625, 280017, 5764801, 134219264, 3486784428, 100000031250, 3138428376721, 106993206079936, 3937376385699289, 155568095575106627, 6568408355712921875, 295147905179822588160, 14063084452067724991009, 708235345355351624428356, 37589973457545958193355601
a(n) = Sum_{d|n} 2^(d-1) * binomial(d, n/d).
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0
1, 4, 12, 34, 80, 204, 448, 1072, 2308, 5280, 11264, 25088, 53248, 116032, 245920, 527880, 1114112, 2369152, 4980736, 10508880, 22022336, 46193664, 96468992, 201469408, 419430416, 872734720, 1811960832, 3758844096, 7784628224, 16107909312, 33285996544, 68723417856, 141734089728
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