A320432 Expansion of e.g.f. exp(3 * (1 - exp(x)) + x).

1, -2, 1, 7, -8, -65, 37, 1024, 1351, -19001, -92618, 232513, 4087189, 9953926, -123909155, -1170342533, -676144160, 62840385619, 490129709977, -551829062288, -40624407525941, -305175084654341, 698633855671510, 34571970743398621, 278738497423756153, -663168571756087538

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(0) = 1 and a(n) = a(n-1) - 3 * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.

a(n) = exp(3) * Sum_{k>=0} (k + 1)^n * (-3)^k / k!.

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -3). - Vaclav Kotesovec, Jul 06 2020

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[3 * (1 - Exp[x]) + x], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)
Table[Sum[Binomial[n, k] * BellB[k, -3], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(3*(1-exp(x))+x)))

Crossrefs

Column k=3 of A335977.

Cf. A078940, A335981.

Sequence in context: A371261 A199964 A217107 * A141513 A258058 A238223

Adjacent sequences: A320429 A320430 A320431 * A320433 A320434 A320435

Keyword

sign

Author

Seiichi Manyama, Jul 06 2020

Status

approved