OFFSET
0,2
FORMULA
a(n) = Sum_{m=0..n} (-1)^m*A285061(n, m), n >= 0.
E.g.f.: exp(x)*exp(1 - exp(4*x)).
a(n) = e*Sum_{m>=0} ((-1)^m / m!)*(1 + 4*m)^n, n >= 0, (DobiĆski type formula).
a(n) = Sum_{k=0..n} binomial(n, k) * 4^k * A000587(k), n >= 0. - Vaclav Kotesovec, Apr 23 2017
a(0) = 1; a(n) = a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 4^k * a(n-k). - Ilya Gutkovskiy, Nov 30 2023
MATHEMATICA
Table[Sum[Binomial[n, k]*BellB[k, -1]*4^k, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 19 2017 *)
PROG
(Python)
from sympy import bell, binomial
def a(n): return sum([binomial(n, k)*bell(k, -1)*4**k for k in range(n + 1)]) # Indranil Ghosh, May 06 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Apr 13 2017
STATUS
approved