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A355495 Expansion of Sum_{k>=0} (k^2 * x/(1 - x))^k.

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%I A355495 #14 Feb 24 2023 19:04:21
%S A355495 1,1,17,762,67772,10032208,2226273192,691431572992,286268594755712,
%T A355495 152365547943819264,101361042063083269520,82409537565402784477984,
%U A355495 80397802305461995791664944,92692687015689239272783171264
%N A355495 Expansion of Sum_{k>=0} (k^2 * x/(1 - x))^k.
%H A355495 Winston de Greef, <a href="/A355495/b355495.txt">Table of n, a(n) for n = 0..213</a>
%F A355495 a(n) = Sum_{k=1..n} k^(2*k) * binomial(n-1,k-1) for n > 0.
%o A355495 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x/(1-x))^k))
%o A355495 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(2*k)*binomial(n-1, k-1)));
%Y A355495 Cf. A355494, A355496.
%Y A355495 Cf. A323280.
%K A355495 nonn
%O A355495 0,3
%A A355495 _Seiichi Manyama_, Jul 04 2022