OFFSET
0,3
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..352
FORMULA
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*k,n-k)/k!.
E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^2) ). - _ Seiichi Manyama_, Sep 23 2024
MATHEMATICA
Array[#!*Sum[ (# + 1)^(k - 1)*Binomial[2 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*k, n-k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 17 2023
STATUS
approved