A032429 Coefficients of Jacobi elliptic function c(6,m).

1, 896803, 2949965020, 2504055894564, 1171517154238290, 393938089395885894, 107947764316226205276, 25835579116799316507780, 5632500127524872577252027, 1149330973559307337432235521, 223559382769795167319093086664, 41982964485265754951017173213880

Offset: 6

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. A060928 (6th lower diagonal).

Formula

a(n) = T(2*n+1,0,6) 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