A355473 Expansion of Sum_{k>=0} x^k/(1 - k^3 * x)^(k+1).
1, 1, 3, 28, 497, 12736, 517297, 28793248, 2095968065, 199522773568, 23839495688321, 3482169003693304, 616298415199306369, 130134007837039167040, 32272959284595295173377, 9313050358489324003967176, 3101245112865402456422252033
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..235
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^3*x)^(k+1))) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*x^k/k!))) -
PARI
a(n) = sum(k=0, n, k^(3*(n-k))*binomial(n, k));
Formula
E.g.f.: Sum_{k>=0} exp(k^3 * x) * x^k/k!.
a(n) = Sum_{k=0..n} k^(3*(n-k)) * binomial(n,k).