A349088 - OEIS

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A349088

a(n) = n! * Sum_{k=0..floor((n-1)/3)} 1 / (3*k+1)!.

0, 1, 2, 6, 25, 125, 750, 5251, 42008, 378072, 3780721, 41587931, 499055172, 6487717237, 90828041318, 1362420619770, 21798729916321, 370578408577457, 6670411354394226, 126737815733490295, 2534756314669805900, 53229882608065923900, 1171057417377450325801

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

E.g.f.: (exp(x) - 2 * exp(-x/2) * sin((Pi - 3*sqrt(3)*x)/6)) / (3*(1 - x)).

a(n) = floor(c * n!) for n > 0, where c = 1.041865355... = A143820.

MATHEMATICA

Table[n! Sum[1/(3 k + 1)!, {k, 0, Floor[(n - 1)/3]}], {n, 0, 22}]

nmax = 22; CoefficientList[Series[(Exp[x] - 2 Exp[-x/2] Sin[(Pi - 3 Sqrt[3] x)/6])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS