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A355495 Expansion of Sum_{k>=0} (k^2 * x/(1 - x))^k. 3

%I #14 Feb 24 2023 19:04:21

%S 1,1,17,762,67772,10032208,2226273192,691431572992,286268594755712,

%T 152365547943819264,101361042063083269520,82409537565402784477984,

%U 80397802305461995791664944,92692687015689239272783171264

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

%H Winston de Greef, <a href="/A355495/b355495.txt">Table of n, a(n) for n = 0..213</a>

%F a(n) = Sum_{k=1..n} k^(2*k) * binomial(n-1,k-1) for n > 0.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x/(1-x))^k))

%o (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(2*k)*binomial(n-1, k-1)));

%Y Cf. A355494, A355496.

%Y Cf. A323280.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 04 2022

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Last modified April 12 14:01 EDT 2024. Contains 371635 sequences. (Running on oeis4.)