A348597 a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (3*k)!.

1, 1, 2, 5, 20, 100, 601, 4207, 33656, 302903, 3029030, 33319330, 399831961, 5197815493, 72769416902, 1091541253529, 17464660056464, 296899220959888, 5344185977277985, 101539533568281715, 2030790671365634300, 42646604098678320299, 938225290170923046578

Offset: 0

Author

Ilya Gutkovskiy, Mar 25 2022

Keywords

• nonn

Crossrefs

Cf. A000166, A009102, A346441, A349087, A352659.

Programs

Mathematica

Table[n! Sum[(-1)^k/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Exp[-x] + 2 Exp[x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: (exp(-x) + 2 * exp(x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).

a(n) = round(c * n!), where c = 0.834719468... = A346441.