OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..386
FORMULA
a(n) = (2*n)!/n! * [x^(2*n)] ((1+x)*log(1+x))^n.
a(n) = Sum_{j=0..n} binomial(n+j,n) * n^j * Stirling1(2*n,n+j).
MAPLE
b:= proc(n, k) option remember; `if`(n=k, 1, `if`(k=0, 0,
(n-1)*b(n-2, k-1)+b(n-1, k-1)+(k-n+1)*b(n-1, k)))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..25);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == k, 1, If[k == 0, 0,
(n-1) b[n-2, k-1] + b[n-1, k-1] + (k-n+1) b[n-1, k]]];
a[n_] := b[2n, n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 01 2023, from Maple code *)
CROSSREFS
KEYWORD
sign
AUTHOR
Alois P. Heinz, Jan 20 2018
STATUS
approved