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A320433 Expansion of e.g.f. exp(4 * (1 - exp(x)) + x). 1
1, -3, 5, 5, -43, -27, 597, 805, -11883, -40475, 265685, 2133157, -3405803, -107760283, -301542315, 4458255397, 42421260949, -45046794011, -3365690666283, -19844416105563, 138274174035221, 2917746747446373, 11092963732101461, -207438902364296411, -3205301465165742187 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(0) = 1 and a(n) = a(n-1) - 4 * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.

a(n) = exp(4) * Sum_{k>=0} (k + 1)^n * (-4)^k / k!.

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -4). - Vaclav Kotesovec, Jul 06 2020

MATHEMATICA

m = 24; Range[0, m]! * CoefficientList[Series[Exp[4 * (1 - Exp[x]) + x], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)

Table[Sum[Binomial[n, k] * BellB[k, -4], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)

PROG

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(4*(1-exp(x))+x)))

CROSSREFS

Column k=4 of A335977.

Cf. A078945, A335982.

Sequence in context: A072624 A147976 A019247 * A165142 A231809 A186969

Adjacent sequences:  A320430 A320431 A320432 * A320434 A320435 A320436

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 06 2020

STATUS

approved

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Last modified March 7 21:10 EST 2021. Contains 341933 sequences. (Running on oeis4.)