Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Jun 11 2018 05:11:38
%S -744,80256,-12288744,2126816256,-392642298600,75506620496256,
%T -14935073808384744,3015675387953504256,-618587635244888064744,
%U 128473308888136855075200,-26951900214112779571200744
%N Euler transform is 1 / (q j(q)) where j is j-function (A000521).
%H Seiichi Manyama, <a href="/A192731/b192731.txt">Table of n, a(n) for n = 1..424</a>
%H B. Brent, <a href="http://mathoverflow.net/questions/69365/">p-adic continuity for exponents in product decomposition of the j-invariant</a>, Answer 3 by W. Zudilin
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F 1 / (q j(q)) = Product_{k>0} (1 - x^k)^-a(k).
%F a(n) = 3*(A110163(n) - 8) = (1/n) * Sum_{d|n} A008683(n/d) * A288261(d). - _Seiichi Manyama_, Jun 18 2017
%F a(n) ~ (-1)^n * 3*exp(Pi*sqrt(3)*n) / n. - _Vaclav Kotesovec_, Mar 24 2018
%e From _Seiichi Manyama_, Jun 18 2017: (Start)
%e a(1) = (1/1) * A008683(1/1) * A288261(1) = (1/1) * (-744) = -744,
%e a(2) = (1/2) * (A008683(2/1) * A288261(1) + A008683(2/2) * A288261(2)) = (1/2) * (744 + 159768) = 80256. (End)
%o (PARI) {a(n) = local(A, S); if( n<1, 0, A = 1 + x * O(x^n); S = x * ellj( x * A ); for( k = 1, n-1, S *= (A - x^k) ^ polcoeff( S, k)); - polcoeff( S, n))}
%Y Cf. A008683, A063995, A110163, A192732, A288261, A302407, A305757.
%K sign
%O 1,1
%A _Michael Somos_, Jul 08 2011