A360833 Expansion of Sum_{k>=0} ( k * x / (1 - (k * x)^3) )^k.
1, 1, 4, 27, 257, 3189, 48843, 889080, 18731109, 448004763, 11987812504, 354763577414, 11503684020051, 405589341060930, 15447798292502206, 632069580794524857, 27649951709582591394, 1287748889361331630661, 63616184683123273364961
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x/(1-(k*x)^3))^k)) -
PARI
a(n) = sum(k=0, n\3, (n-3*k)^n*binomial(n-2*k-1, k));
Formula
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n * binomial(n-2*k-1,k).