A318121 a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).

1, 1, 4, 15, 65, 269, 1205, 5325, 24064, 108849, 496790, 2275492, 10470720, 48325984, 223721404, 1038182441, 4828274432, 22497132116, 105001996350, 490816448220, 2297356108318, 10766317435860, 50511178395306, 237217429972191, 1115084064063866, 5246116796164594

Offset

0,3

Comments

For n > 2, a(n) is the n-th term of the Euler transform of n-gonal pyramidal numbers.

Links

Table of n, a(n) for n=0..25.

N. J. A. Sloane, Transforms

Index to sequences related to pyramidal numbers

Formula

a(n) ~ c * d^n / sqrt(n), where d = 4.80064986801984997726284... and c = 0.244706939300168165858... - Vaclav Kotesovec, Aug 19 2018

Mathematica

Table[SeriesCoefficient[Exp[Sum[x^k (1 + (n - 3) x^k)/(k (1 - x^k)^4), {k, 1, n}]], {x, 0, n}], {n, 0, 25}]

Crossrefs

Cf. A000335, A279215, A279216, A279217, A279218, A279219, A318118.

Sequence in context: A007526 A233536 A349202 * A357785 A369229 A097422

Adjacent sequences: A318118 A318119 A318120 * A318122 A318123 A318124

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 18 2018

Status

approved