OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
MATHEMATICA
With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[2*x*Cosh[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*x*cosh(x))))
(PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 25 2022
STATUS
approved