A032428 Coefficients of Jacobi elliptic function c(5,m).

1, 99642, 116294673, 47152124264, 11966116940238, 2347836365864484, 393938089395885894, 59752013018382750024, 8470841585571575617239, 1146456994425541774291534, 150221961163114696686151695, 19239380962379456298762250416, 2424371762015227695363084225932

Offset: 5

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.
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A060928 (5th lower diagonal).

Formula

a(n) = T(2*n+1,0,5) 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