A360818 Expansion of Sum_{k>=0} ( (k*x)^2 / (1 - k*x) )^k.
1, 0, 1, 1, 17, 65, 922, 7074, 106183, 1248479, 21144289, 331763177, 6441011484, 124904347404, 2773880604749, 63538143151589, 1600211849569585, 42076439530000297, 1189408501356380558, 35214128238218917974, 1106088535644470694779
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, ((k*x)^2/(1-k*x))^k)) -
PARI
a(n) = sum(k=0, n\2, k^n*binomial(n-k-1, n-2*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} k^n * binomial(n-k-1,n-2*k).