A305654 a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + x^k)/(k*(1 - x^k)^n)).

1, 1, 4, 14, 65, 323, 1890, 12002, 83901, 630818, 5081318, 43546333, 395422430, 3788368227, 38151667046, 402516707510, 4436230390977, 50948789415297, 608433141666219, 7540823673023319, 96826154085714992, 1285991546051286085, 17640769457638701839, 249602608552024560609

Offset

0,3

Links

Table of n, a(n) for n=0..23.

N. J. A. Sloane, Transforms

Formula

a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^(2*binomial(n+k-2,n-1)-binomial(n+k-3,n-2)).

Mathematica

Table[SeriesCoefficient[Exp[Sum[x^k (1 + x^k)/(k (1 - x^k)^n), {k, 1, n}]], {x, 0, n}], {n, 0, 23}]
Table[SeriesCoefficient[Product[1/(1 - x^k)^(2 Binomial[n + k - 2, n - 1] - Binomial[n + k - 3, n - 2]), {k, 1, n}], {x, 0, n}], {n, 0, 23}]

Crossrefs

Cf. A000990, A023871, A253289, A279215, A293554, A305206, A305653, A305655.

Sequence in context: A020041 A081891 A119857 * A241465 A320488 A126787

Adjacent sequences: A305651 A305652 A305653 * A305655 A305656 A305657

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 07 2018

Status

approved