A032433 Coefficients of Jacobi elliptic function c(10,m).

1, 5883948671, 1163848723925346, 15875718186751193446, 67362921649153881472361, 150221961163114696686151695, 223559382769795167319093086664, 252583298644057469403578416269848, 234170438234669757816987374536542702, 187377221472810770345920109207417275058

Offset: 10

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 (10th lower diagonal).

Formula

a(n) = T(2*n+1,0,10) 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