OFFSET
0,4
FORMULA
a(n) = n! * [x^n] (1 + sinh(x))/(2 - cosh(x)).
a(n) = Sum_{j=0..n-1,2} binomial(n, j) * a(j) for n > 0, a(0) = 1. (Note that the sum runs in steps of 2.)
a(n) ~ n! * (1 + 1/sqrt(3) + (-1)^n * (-1 + 1/sqrt(3))) / log(2 + sqrt(3))^(n+1). - Vaclav Kotesovec, Sep 02 2024
MAPLE
a := proc(n) option remember; local j;
ifelse(n = 0, 1, add(binomial(n, j) * a(j), j = 0..n-1, 2)) end:
# Or:
gf := (exp(-x) - exp(x) - 2)/(exp(-x) + exp(x) - 4):
series(gf, x, 24): seq(n!*coeff(%, x, n), n = 0..23);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 25 2024
STATUS
approved