A032431 Coefficients of Jacobi elliptic function c(8,m).

1, 72641337, 1859539731885, 6460701405171285, 9412382749388124015, 8470841585571575617239, 5632500127524872577252027, 3051808875538951440990525939, 1429953329302734392093044646982, 602297594518030428986818986545686, 234170438234669757816987374536542702

Offset: 8

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 (8th lower diagonal).

Formula

a(n) = T(2*n+1,0,8) where T(1,0,0) = 1; T(n,i,j) = 0 if i+j < 0 or i+j > n/2; T(2*n,i,j) = (2*j+1) * T(2*n-1,i,j) + (2*i+2) * T(2*n-1,i+1,j-1) + (2*n-2*i-2*j+1) * T(2*n-1,i,j-1), and T(2*n+1,i,j) = (2*i+1) * T(2*n-1,i,j) + (2*j+2) * T(2*n,i-1,j+1) + (2*n-2*i-2*j+2) * T(2*n-1,i-1,j). - Sean A. Irvine, Jun 20 2020

Extensions

Offset corrected and more terms from Sean A. Irvine, Jun 20 2020