A360819 Expansion of Sum_{k>=0} ( (k*x)^3 / (1 - k*x) )^k.
1, 0, 0, 1, 1, 1, 65, 257, 769, 21732, 182268, 1075171, 22120299, 292415838, 2784944366, 52394511682, 914813711338, 12411977351379, 240868108545883, 5024364548461861, 88977315031536205, 1888119425325238979, 44744897995532996819, 971263427084750362992
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, ((k*x)^3/(1-k*x))^k)) -
PARI
a(n) = sum(k=0, n\3, k^n*binomial(n-2*k-1, n-3*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} k^n * binomial(n-2*k-1,n-3*k).