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A192732 A weight 1/2 meromorphic modular form associated with the j-function. 3

%I

%S 3,0,0,0,-744,0,0,80256,-257985,0,0,5121792,-12288744,0,0,132991488,

%T -275853438,0,0,2126816256,-4031741952,0,0,24832604160,-44199075375,0,

%U 0,231276864000,-392642298600,0,0,1812417804288,-2964679005375

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

%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

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

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

%o (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))}

%Y Cf. A192731.

%K sign

%O -3,1

%A _Michael Somos_, Jul 08 2011

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)