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A318121
a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).
1
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.
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 18 2018
STATUS
approved