A192732 A weight 1/2 meromorphic modular form associated with the j-function.

3, 0, 0, 0, -744, 0, 0, 80256, -257985, 0, 0, 5121792, -12288744, 0, 0, 132991488, -275853438, 0, 0, 2126816256, -4031741952, 0, 0, 24832604160, -44199075375, 0, 0, 231276864000, -392642298600, 0, 0, 1812417804288, -2964679005375

Offset

-3,1

Links

Table of n, a(n) for n=-3..29.

B. Brent, p-adic continuity for exponents in product decomposition of the j-invariant Answer 3 by W. Zudilin

Formula

a(n^2) = A192731(n).

Example

3/q^3 - 744*q + 80256*q^4 - 257985*q^5 + 5121792*q^8 - 12288744*q^9 + ...

Prog

(PARI) {a(n) = local( A, F, t, T, E); if( n<-3, 0, n += 4; A = x * O(x^n); t = sum( k= 1, sqrtint( n), 2 * x^k^2, 1 + A); T = t^20; E = sum( k= 1, n\4, -264 * sigma( k, 9) * x^(4*k), 1 + A); polcoeff( (( E / T )' * T / eta( x^4 + A)^24 + 1216*x^3) * -3/40 * t, n-1))}

Crossrefs

Cf. A192731.

Sequence in context: A057387 A109898 A223074 * A092573 A307801 A186717

Adjacent sequences: A192729 A192730 A192731 * A192733 A192734 A192735

Keyword

sign

Author

Michael Somos, Jul 08 2011

Status

approved