A024218 a(n) = s(1)*s(2)*...*s(n+1)(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c=(-1)^n+1 and s(k) = 3k-2 for k = 1,2,3,...

1, 3, 58, 474, 11224, 155016, 4516912, 88578480, 3088805440, 78711944640, 3204477861760, 100604441589120, 4688743517516800, 175033337095142400, 9194586775173990400, 397954301618843289600, 23270065752049280819200, 1145878628833500097536000

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A024397.

Programs

Mathematica

Table[Product[3*k - 2, {k, 1, n+1}] * Sum[(-1)^k/(3*k - 2), {k, 2, n+1}], {n, 1, 20}] (* Vaclav Kotesovec, Jan 02 2020 *)

PARI

a(n)={my(s=vector(n+1, k, 3*k-2)); vecprod(s)*sum(k=2, #s, (-1)^k/s[k])} \\ Andrew Howroyd, Jan 01 2020

Formula

a(n) ~ sqrt(2*Pi) * (9 - sqrt(3)*Pi - 3*log(2)) * 3^(n - 1) * n^(n + 5/6) / (Gamma(1/3) * exp(n)). - Vaclav Kotesovec, Jan 02 2020

Extensions

Terms a(13) and beyond from Andrew Howroyd, Jan 01 2020