A192731 Euler transform is 1 / (q j(q)) where j is j-function (A000521).

-744, 80256, -12288744, 2126816256, -392642298600, 75506620496256, -14935073808384744, 3015675387953504256, -618587635244888064744, 128473308888136855075200, -26951900214112779571200744

Offset: 1

Author

Michael Somos, Jul 08 2011

Keywords

• sign

Examples

			From _Seiichi Manyama_, Jun 18 2017: (Start)
a(1) = (1/1) * A008683(1/1) * A288261(1) = (1/1) * (-744) = -744,
a(2) = (1/2) * (A008683(2/1) * A288261(1) + A008683(2/2) * A288261(2)) = (1/2) * (744 + 159768) = 80256. (End)
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..424
• B. Brent, p-adic continuity for exponents in product decomposition of the j-invariant, Answer 3 by W. Zudilin
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A008683, A063995, A110163, A192732, A288261, A302407, A305757.

Programs

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))}

Formula

1 / (q j(q)) = Product_{k>0} (1 - x^k)^-a(k).

a(n) = 3*(A110163(n) - 8) = (1/n) * Sum_{d|n} A008683(n/d) * A288261(d). - Seiichi Manyama, Jun 18 2017

a(n) ~ (-1)^n * 3*exp(Pi*sqrt(3)*n) / n. - Vaclav Kotesovec, Mar 24 2018