OFFSET
0,3
COMMENTS
The "Stirling-Bernoulli transform" maps a sequence b_0, b_1, b_2, ... to a sequence c_0, c_1, c_2, ..., where if B has o.g.f. B(x), c has e.g.f. exp(x)*B(1-exp(x)). More explicitly, c_n = Sum_{m=0..n} (-1)^m*m!*Stirling2(n+1,m+1)*b_m.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
MAPLE
a:= n-> add((-1)^k *k! *Stirling2(n+1, k+1)*binomial(2*k, k)/
(k+1), k=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, May 17 2013
MATHEMATICA
a[n_] := Sum[(-1)^k k! StirlingS2[n+1, k+1] CatalanNumber[k], {k, 0, n}];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Apr 06 2016 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Dec 09 1999
STATUS
approved