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%I #25 Jul 31 2021 07:19:37
%S 1,0,2,24,228,2400,30360,453600,7702800,144910080,2981089440,
%T 66561264000,1603358729280,41434803970560,1142808612865920,
%U 33485770103385600,1038238875100627200,33945895488708403200,1166858228814204326400,42055660151648798054400
%N E.g.f.: exp(Sum_{k>=1} (k-1)^2*x^k).
%H Seiichi Manyama, <a href="/A288270/b288270.txt">Table of n, a(n) for n = 0..421</a>
%F a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} (k-1)^2*k*a(n-k)/(n-k)! for n > 0.
%F E.g.f.: exp(x^2*(1 + x)/(1 - x)^3). - _Ilya Gutkovskiy_, Jul 27 2020
%F a(n) ~ 2^(-7/8) * 3^(1/8) * n^(n - 1/8) / exp(n - 2^(9/4)*n^(3/4)/3^(3/4) + sqrt(2*n/3) - 2^(3/4)*n^(1/4)/3^(5/4) + 13/54). - _Vaclav Kotesovec_, Jul 31 2021
%o (PARI) {a(n) = n!*polcoeff(exp(sum(k=1, n, (k-1)^2*x^k)+x*O(x^n)), n)}
%Y E.g.f.: exp(Sum_{k>=1} (k-1)^m*x^k): A000262 (m=0), A052887 (m=1), this sequence (m=2), A290690 (m=3).
%Y Cf. A255807.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 20 2017