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

%I

%S 1,6,15,43,105,271,633,1501,3389,7598,16561,35710,75444,157618,324291,

%T 659949,1326571,2640033,5199264,10147142,19624563,37643761,71629723,

%U 135288468,253682683,472470635,874204574,1607506045,2938259227,5340032114,9651674965

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

%H Vaclav Kotesovec, <a href="/A137806/b137806.txt">Table of n, a(n) for n = 1..2000</a>

%F 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

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Apr 08 2010, following a suggestion from _Gary W. Adamson_

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Last modified July 30 18:28 EDT 2021. Contains 346359 sequences. (Running on oeis4.)