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A352647
Expansion of e.g.f. 1/(1 - 3 * x * cos(x)).
2
1, 3, 18, 153, 1728, 24315, 410400, 8079729, 181786752, 4601232243, 129402385920, 4003157532297, 135098815002624, 4939266681129963, 194472450526169088, 8203835046344538465, 369151362125290045440, 17649035213360472293091, 893431062200523039178752
OFFSET
0,2
LINKS
FORMULA
a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
MATHEMATICA
With[{m = 18}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*x*Cos[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*x*cos(x))))
(PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 25 2022
STATUS
approved