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

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

Cf. A002627, A009628, A143820, A186763, A337725, A349089, A352659.

Sequence in context: A370511 A074010 A352660 * A030806 A030828 A030839

Adjacent sequences: A349085 A349086 A349087 * A349089 A349090 A349091

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 25 2022

Status

approved