OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Pochhammer Symbol.
FORMULA
a(n) = n! * [x^n] cosh( sqrt(n) * log(1-x) ).
a(n) = ( (sqrt(n))_n + (-sqrt(n))_n )/2, where (x)_n is the Pochhammer symbol.
a(n) ~ n^(n + sqrt(n)/2 - 1/4) / (2*exp(n - sqrt(n) - 1/2)) * (1 - 3/(4*sqrt(n))). - Vaclav Kotesovec, Oct 10 2022
PROG
(PARI) a(n) = sum(k=0, n\2, n^k*abs(stirling(n, 2*k, 1)));
(PARI) a(n) = round(n!*polcoef(cosh(sqrt(n)*log(1-x+x*O(x^n))), n));
(PARI) a(n) = round((prod(k=0, n-1, sqrt(n)+k)+prod(k=0, n-1, -sqrt(n)+k)))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 09 2022
STATUS
approved