A137806 Euler transform of 1, 5, 9, 13, 17, 21, 25, 29, 33, ... (A016813).

1, 6, 15, 43, 105, 271, 633, 1501, 3389, 7598, 16561, 35710, 75444, 157618, 324291, 659949, 1326571, 2640033, 5199264, 10147142, 19624563, 37643761, 71629723, 135288468, 253682683, 472470635, 874204574, 1607506045, 2938259227, 5340032114, 9651674965

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..2000

Formula

a(n) ~ 2^(1/3) * Pi / (sqrt(3) * A^4 * n^(5/18) * Zeta(3)^(2/9)) * exp(1/3 - Pi^4/(192*Zeta(3)) - n^(1/3)*Pi^2/(4*Zeta(3)^(1/3)) + 3*n^(2/3)*Zeta(3)^(1/3)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 07 2015

Mathematica

Rest[CoefficientList[Series[Product[1/(1-x^k)^(4*k-3), {k, 1, 30}], {x, 0, 30}], x]] (* Vaclav Kotesovec, Aug 07 2015 *)

Crossrefs

Sequence in context: A271809 A272289 A272320 * A193449 A197160 A182420

Adjacent sequences: A137803 A137804 A137805 * A137807 A137808 A137809

Keyword

nonn

Author

N. J. A. Sloane, Apr 08 2010, following a suggestion from Gary W. Adamson

Status

approved