OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * a(n-2*k-1).
a(n) ~ n! / (2^(3/2) * arcsin(1/3)^(n+1)). - Vaclav Kotesovec, Mar 26 2022
MATHEMATICA
With[{m = 17}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*Sin[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*sin(x))))
(PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n, 2*k+1)*a(n-2*k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 25 2022
STATUS
approved