A360933 Expansion of e.g.f. Sum_{k>=0} exp((3^k - 1)*x) * x^k/k!.
1, 1, 5, 37, 521, 12361, 510605, 35837677, 4348414481, 903630399121, 325415100648725, 201805338104622517, 217331913727442676761, 404193405278758441895641, 1306527408146744068362681245, 7302236837745565755664036677757
Offset: 0
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((3^k-1)*x)*x^k/k!))) -
PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(3^k-1)*x)^(k+1))) -
PARI
a(n) = sum(k=0, n, (3^k-1)^(n-k)*binomial(n, k));
Formula
G.f.: Sum_{k>=0} x^k/(1 - (3^k - 1)*x)^(k+1).
a(n) = Sum_{k=0..n} (3^k - 1)^(n-k) * binomial(n,k).