OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..547
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
E.g.f.: cosh( 3 * (exp(x) - 1) ).
a(n) = Sum_{k=0..floor(n/2)} 9^k * Stirling2(n,2*k).
a(n) = ( Bell_n(3) + Bell_n(-3) )/2, where Bell_n(x) is n-th Bell polynomial.
a(n) = 1; a(n) = 9 * Sum_{k=0..n-1} binomial(n-1, k) * A357668(k).
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(cosh(3*(exp(x)-1))))
(PARI) a(n) = sum(k=0, n\2, 9^k*stirling(n, 2*k, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, 3)+Bell_poly(n, -3)))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 08 2022
STATUS
approved