A356827 Expansion of e.g.f. exp(x * exp(3*x)).

1, 1, 7, 46, 361, 3436, 37729, 463366, 6280369, 93015352, 1491337441, 25684077706, 472217487625, 9221588527204, 190441412508481, 4143470377262806, 94663498086222049, 2264440394856702832, 56570146384760433217, 1472545685988162638722

Offset: 0

Author

Seiichi Manyama, Aug 29 2022

Keywords

• nonn

Crossrefs

Cf. A000248, A003725, A216689, A295552.

Cf. A277456, A336951, A351737, A355501, A356820.

Programs

Maple

A356827 := proc(n)
    add((3*k)^(n-k) * binomial(n,k),k=0..n) ;
end proc:
seq(A356827(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(3*x))))

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-3*k*x)^(k+1)))

PARI

a(n) = sum(k=0, n, (3*k)^(n-k)*binomial(n, k));

Formula

G.f.: Sum_{k>=0} x^k / (1 - 3*k*x)^(k+1).

a(n) = Sum_{k=0..n} (3*k)^(n-k) * binomial(n,k).