OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..236
FORMULA
a(n) == 0 (mod 2) for n > 0.
a(n) = (n!)^2 * [(x*y)^n] 1 / (exp(x) + exp(y) - exp(x+y))^2.
a(n) ~ sqrt(Pi) * n^(2*n + 3/2) / (4 * sqrt(1 - log(2)) * exp(2*n) * log(2)^(2*n+2)). - Vaclav Kotesovec, Apr 13 2025
MAPLE
f:= proc(n) local k; add(k!*(k+1)!*Stirling2(n, k)^2, k=0..n) end proc:
map(f, [$0..40]);
MATHEMATICA
Table[Sum[k! * (k+1)! * StirlingS2[n, k]^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 13 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*(k+1)!*stirling(n, k, 2)^2);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 04 2025
STATUS
approved
