A365971 Expansion of e.g.f. exp( Sum_{k>=0} x^(3*k+2) / (3*k+2) ).

1, 0, 1, 0, 3, 24, 15, 504, 5145, 9072, 300321, 3795120, 12284811, 441965160, 6672128463, 33017539464, 1306646813745, 22946632267104, 156924556846785, 6810382180903392, 136393286581031571, 1209571612450077240, 57211108821810731151, 1286884543482633415320

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A000166, A365972.

Cf. A365978.

Programs

Mathematica

nmax = 20; CoefficientList[Series[(1 + x + x^2)^(1/6) / (E^(ArcTan[Sqrt[3]*x/(2 + x)]/Sqrt[3]) * (1-x)^(1/3)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 30 2024 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\3, x^(3*k+2)/(3*k+2)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-2)/3)} a(n-3*k-2)/(n-3*k-2)!.