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Euler transform of A027656(n-1).
23

%I #21 Nov 17 2021 08:23:55

%S 0,1,1,3,3,6,9,13,19,28,42,57,84,115,164,227,313,429,588,799,1079,

%T 1461,1952,2617,3480,4627,6111,8072,10604,13905,18181,23701,30828,

%U 39990,51763,66822,86124,110687,142039,181841,232409,296401,377419,479635,608558,770818

%N Euler transform of A027656(n-1).

%C Also the weigh transform of A003602. - _John Keith_, Nov 17 2021

%H Vaclav Kotesovec, <a href="/A035528/b035528.txt">Table of n, a(n) for n = 0..5000</a>

%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], 2015-2016.

%F a(n) ~ A^(1/2) * Zeta(3)^(11/72) * exp(-1/24 - Pi^4/(1728*Zeta(3)) + Pi^2 * n^(1/3)/(3*2^(8/3)*Zeta(3)^(1/3)) + 3*Zeta(3)^(1/3) * n^(2/3)/2^(4/3)) / (sqrt(3*Pi) * 2^(71/72) * n^(47/72)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Oct 02 2015

%t nmax = 50; CoefficientList[Series[-1 + Product[1/(1 - x^(2*k-1))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 19 2015 *)

%t nmax = 100; Flatten[{0, Rest[CoefficientList[Series[E^Sum[1/j*x^j/(1 - x^(2*j))^2, {j, 1, nmax}], {x, 0, nmax}], x]]}] (* _Vaclav Kotesovec_, Oct 10 2015 *)

%Y Cf. A000219, A003602, A052847, A263150, A263352, A262876, A263136, A263141.

%K nonn

%O 0,4

%A _Christian G. Bower_