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A356827
Expansion of e.g.f. exp(x * exp(3*x)).
1
1, 1, 7, 46, 361, 3436, 37729, 463366, 6280369, 93015352, 1491337441, 25684077706, 472217487625, 9221588527204, 190441412508481, 4143470377262806, 94663498086222049, 2264440394856702832, 56570146384760433217, 1472545685988162638722
OFFSET
0,3
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).
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
PROG
(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));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 29 2022
STATUS
approved