A356820 - OEIS

%I #12 Feb 23 2023 18:03:08

%S 1,-1,-5,-10,73,1004,5473,-15562,-746447,-9174088,-41916959,823985546,

%T 24629093641,335144105828,1248594602305,-67564407472426,

%U -2160461588461343,-34957074099518608,-154556217713939903,10500560586914149250,409146670525578079801

%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} (-1)^k * (3*k)^(n-k) * binomial(n,k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*exp(3*x))))

%o (PARI) my(N=30, 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, (-1)^k*(3*k)^(n-k)*binomial(n, k));

%Y Cf. A292952, A356813, A356819.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 29 2022