A024397 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-1 for k = 1,2,3,...

2, 6, 146, 1164, 32108, 432720, 14141360, 271332960, 10373558240, 259311694080, 11400458720000, 351858201408000, 17517836995904000, 644027147554560000, 35846613866733824000, 1530195810548224512000, 94207122098479233536000, 4580941398125400354816000

Offset

1,1

Links

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

Formula

a(n) ~ Gamma(1/3) * (9 - 2*Pi*sqrt(3) + 6*log(2)) * 3^(n - 1/2) * n^(n + 7/6) / (2^(3/2) * sqrt(Pi) * exp(n)). - Vaclav Kotesovec, Jan 02 2020

Mathematica

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

Prog

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

Crossrefs

Cf. A024218, A024384.

Sequence in context: A164764 A333444 A274986 * A099185 A015173 A122570

Adjacent sequences: A024394 A024395 A024396 * A024398 A024399 A024400

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 01 2020

Status

approved