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Coefficients of Jacobi elliptic function c(6,m).
1

%I #20 Jul 09 2022 11:08:03

%S 1,896803,2949965020,2504055894564,1171517154238290,

%T 393938089395885894,107947764316226205276,25835579116799316507780,

%U 5632500127524872577252027,1149330973559307337432235521,223559382769795167319093086664,41982964485265754951017173213880

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

%H A. Fransen, <a href="http://dx.doi.org/10.1090/S0025-5718-1981-0628708-X">Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k)</a>, Math. Comp., 37 (1981), 475-497.

%F 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

%Y Cf. A060928 (6th lower diagonal).

%K nonn

%O 6,2

%A _Simon Plouffe_.

%E Offset corrected and more terms from _Sean A. Irvine_, Jun 20 2020