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%I #5 Aug 19 2018 07:22:40
%S 1,1,4,15,65,269,1205,5325,24064,108849,496790,2275492,10470720,
%T 48325984,223721404,1038182441,4828274432,22497132116,105001996350,
%U 490816448220,2297356108318,10766317435860,50511178395306,237217429972191,1115084064063866,5246116796164594
%N a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).
%C For n > 2, a(n) is the n-th term of the Euler transform of n-gonal pyramidal numbers.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F a(n) ~ c * d^n / sqrt(n), where d = 4.80064986801984997726284... and c = 0.244706939300168165858... - _Vaclav Kotesovec_, Aug 19 2018
%t 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}]
%Y Cf. A000335, A279215, A279216, A279217, A279218, A279219, A318118.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 18 2018