OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(n) = n! * [x^n] cosh( sqrt(n) * (exp(x) - 1) ).
a(n) = ( Bell_n(sqrt(n)) + Bell_n(-sqrt(n)) )/2, where Bell_n(x) is n-th Bell polynomial.
PROG
(PARI) a(n) = sum(k=0, n\2, n^k*stirling(n, 2*k, 2));
(PARI) a(n) = round(n!*polcoef(cosh(sqrt(n)*(exp(x+x*O(x^n))-1)), n));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, sqrt(n))+Bell_poly(n, -sqrt(n))))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 09 2022
STATUS
approved