OFFSET
0,2
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 06 2020
STATUS
approved