A355397 Expansion of e.g.f. exp(exp(3*x)/3 + exp(2*x)/2 - 5/6).

1, 2, 9, 51, 350, 2799, 25373, 255854, 2831177, 34023919, 440414146, 6099346455, 89873849705, 1402403637418, 23081230257449, 399284248276827, 7238080522101270, 137125745341692863, 2708536196071195365, 55660194042713099510, 1187724805063462045289

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (3^(k-1) + 2^(k-1)) * binomial(n-1,k-1) * a(n-k).

a(n) ~ exp(exp(3*r)/3 + exp(2*r)/2 - 5/6 - n) * (n/r)^(n + 1/2) / sqrt((1 + 3*r)*exp(3*r) + (1 + 2*r)*exp(2*r)), where r = LambertW(3*n)/3 - 1/(2 + 3/LambertW(3*n) + 3^(4/3) * n^(1/3) * (1 + LambertW(3*n)) / LambertW(3*n)^(4/3)). - Vaclav Kotesovec, Jul 05 2022

Mathematica

nmax = 20; CoefficientList[Series[Exp[Exp[3*x]/3 + Exp[2*x]/2 - 5/6], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 30 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(3*x)/3+exp(2*x)/2-5/6)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (3^(j-1)+2^(j-1))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A355380.

Sequence in context: A277378 A026945 A246464 * A009310 A091319 A193465

Adjacent sequences: A355394 A355395 A355396 * A355398 A355399 A355400

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2022

Status

approved