A032430 Coefficients of Jacobi elliptic function c(7,m).

1, 8071256, 74197080276, 128453495887560, 107266611330420090, 59752013018382750024, 25835579116799316507780, 9424979520638053300516632, 3051808875538951440990525939, 906467723949073501017465886864, 252583298644057469403578416269848

Offset

7,2

Links

Table of n, a(n) for n=7..17.

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

Formula

a(n) = T(2*n+1,0,7) 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

Crossrefs

Cf. A060628 (7th lower diagonal).

Sequence in context: A204970 A185929 A268334 * A206020 A263072 A353540

Adjacent sequences: A032427 A032428 A032429 * A032431 A032432 A032433

Keyword

nonn

Author

Simon Plouffe

Extensions

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

Status

approved