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%I #17 Dec 04 2023 06:29:10
%S 1,1,7,46,361,3436,37729,463366,6280369,93015352,1491337441,
%T 25684077706,472217487625,9221588527204,190441412508481,
%U 4143470377262806,94663498086222049,2264440394856702832,56570146384760433217,1472545685988162638722
%N Expansion of e.g.f. exp(x * exp(3*x)).
%F G.f.: Sum_{k>=0} x^k / (1 - 3*k*x)^(k+1).
%F a(n) = Sum_{k=0..n} (3*k)^(n-k) * binomial(n,k).
%p A356827 := proc(n)
%p add((3*k)^(n-k) * binomial(n,k),k=0..n) ;
%p end proc:
%p seq(A356827(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(3*x))))
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-3*k*x)^(k+1)))
%o (PARI) a(n) = sum(k=0, n, (3*k)^(n-k)*binomial(n, k));
%Y Cf. A000248, A003725, A216689, A295552.
%Y Cf. A277456, A336951, A351737, A355501, A356820.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 29 2022