OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..558
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * Stirling2(n,2*k+1).
a(n) = ( Bell_n(2) - Bell_n(-2) )/4, where Bell_n(x) is n-th Bell polynomial.
a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A065143(k).
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(2*(exp(x)-1))/2)))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^k*stirling(n, 2*k+1, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, 2)-Bell_poly(n, -2)))/4;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 05 2022
STATUS
approved