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A270922 Coefficient of x^n in Product_{k>=1} (1 + x^k)^(k*n). 10
1, 1, 5, 28, 141, 751, 4064, 22198, 122381, 679375, 3792155, 21263331, 119679000, 675763232, 3826165838, 21715370653, 123502583565, 703694143160, 4016079632039, 22953901314649, 131366012754691, 752709483123304, 4317601694413683, 24790635783551008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 5.86811560195778704624328861800917668... and c = 0.25351514412215050116013727161633502...

a(n) = [x^n] exp(n*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018

MATHEMATICA

Table[SeriesCoefficient[Product[(1+x^k)^(k*n), {k, 1, n}], {x, 0, n}], {n, 0, 25}]

CROSSREFS

Cf. A255672, A270913, A270917, A270924.

Sequence in context: A272319 A297322 A037591 * A037682 A271686 A272288

Adjacent sequences:  A270919 A270920 A270921 * A270923 A270924 A270925

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 26 2016

STATUS

approved

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)