A032348 Coefficients of Jacobi function c(3,m).

1, 1228, 165826, 13180268, 834687179, 47152124264, 2504055894564, 128453495887560, 6460701405171285, 321298267540551700, 15875718186751193446, 781562415106660985428, 38396599486084770569951, 1884152729554433297404688

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Links

• A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.

Crossrefs

Cf. A060628 (3rd lower diagonal).

Programs

Mathematica

j = 3; max = 17; coes = CoefficientList[#, k]& /@ ((CoefficientList[ Series[ JacobiSN[x, k], {x, 0, 2*max}], x] // Select[#, # =!= 0 &] &)*Table[(-1)^n*(2*n+1)!, {n, 0, max-1}] ) ; coes[[j+1 ;; -1]][[All, j+1]] (* Jean-François Alcover, May 14 2013 *)

Formula

a(n) = (104*n*9^(n+4) + 3*7^(2*n+7) - (24*n+36)*5^(2*n+7) + (32*n^2+54)*3^(2*n+8) -256*n^3-1248*n^2-1328*n-135) / 12288. - Vaclav Kotesovec after Fransen, Jul 30 2013

Extensions

Typo in a(7) fixed by Jean-François Alcover, May 14 2013