OFFSET
0,2
FORMULA
E.g.f.: (exp(3*x/2) - 2 * sin(sqrt(3)*x/2 + Pi/6)) / (3*exp(x/2) * (1 - x^3)) = x^2/2! + 61*x^5/5! + 20497*x^8/8! + 20292031*x^11/11! + ...
a(n) = floor(c * (3*n+2)!), where c = (exp(3/2) - 2 * sin((3 * sqrt(3) + Pi) / 6))/(3 * sqrt(exp(1))) = A143821.
MATHEMATICA
Table[(3 n + 2)! Sum[1/(3 k + 2)!, {k, 0, n}], {n, 0, 11}]
Table[(3 n + 2)! SeriesCoefficient[(Exp[3 x/2] - 2 Sin[Sqrt[3] x/2 + Pi/6])/(3 Exp[x/2] (1 - x^3)), {x, 0, 3 n + 2}], {n, 0, 11}]
Table[Floor[(Exp[3/2] - 2 Sin[(3 Sqrt[3] + Pi)/6])/(3 Sqrt[Exp[1]]) (3 n + 2)!], {n, 0, 11}]
PROG
(PARI) a(n) = (3*n+2)!*sum(k=0, n, 1/(3*k+2)!); \\ Michel Marcus, Sep 17 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 17 2020
STATUS
approved