OFFSET
0,5
LINKS
Eric Weisstein's MathWorld, Bell Polynomial.
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^(k) * Stirling2(n,2*k+1).
a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357725(k).
a(n) = ( Bell_n(sqrt(2) * i) - Bell_n(-sqrt(2) * i) )/(2 * sqrt(2) * i), where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sin(sqrt(2)*(exp(x)-1))/sqrt(2)))))
(PARI) a(n) = sum(k=0, (n-1)\2, (-2)^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, sqrt(2)*I)-Bell_poly(n, -sqrt(2)*I))/(2*sqrt(2)*I));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 11 2022
STATUS
approved