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A355380 Expansion of e.g.f. exp(exp(3*x) + exp(2*x) - 2). 5
1, 5, 38, 355, 3879, 48050, 661163, 9961745, 162598044, 2851150665, 53350521523, 1059447004560, 22224898346989, 490589320542305, 11356591577861398, 274886065370874775, 6939205217774546339, 182273695066097752170, 4971724931587003394863, 140559648864263508395965 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..463

FORMULA

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

a(0) = 1; a(n) = Sum_{k=1..n} (3^k + 2^k) * binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, Jun 30 2022

a(n) ~ exp(exp(3*z) + exp(2*z) - 2 - n) * (n/z)^(n + 1/2) / sqrt(3*(1 + 3*z)*exp(3*z) + 2*(1 + 2*z)*exp(2*z)), where z = LambertW(n)/3 - 1/(2 + 3/LambertW(n) + 9 * n^(1/3) * (1 + LambertW(n)) / (2*LambertW(n)^(4/3))). - Vaclav Kotesovec, Jul 03 2022

MATHEMATICA

nmax = 20; CoefficientList[Series[Exp[Exp[3*x] + Exp[2*x] - 2], {x, 0, nmax}], x] * Range[0, nmax]!

Table[Sum[Binomial[n, k] * 3^k * 2^(n-k) * BellB[k] * BellB[n-k], {k, 0, n}], {n, 0, 20}]

PROG

(PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(exp(3*x) + exp(2*x) - 2))) \\ Michel Marcus, Jun 30 2022

CROSSREFS

Cf. A143405, A355291, A355381.

Sequence in context: A228657 A113207 A158266 * A213639 A243690 A335530

Adjacent sequences:  A355377 A355378 A355379 * A355381 A355382 A355383

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 30 2022

STATUS

approved

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Last modified October 3 04:11 EDT 2022. Contains 357230 sequences. (Running on oeis4.)