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%I #22 Jul 09 2022 11:07:48
%S 1,1228,165826,13180268,834687179,47152124264,2504055894564,
%T 128453495887560,6460701405171285,321298267540551700,
%U 15875718186751193446,781562415106660985428,38396599486084770569951,1884152729554433297404688
%N Coefficients of Jacobi function c(3,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) = (104*n*9^(n+4) + 3*7^(2*n+7) - (24*n+36)*5^(2*n+7) + (32*n^2+54)*3^(2*n+8) -256*n^3-1248*n^2-1328*n-135) / 12288. - _Vaclav Kotesovec_ after Fransen, Jul 30 2013
%t j = 3; max = 17; coes = CoefficientList[#, k]& /@ ((CoefficientList[ Series[ JacobiSN[x, k], {x, 0, 2*max}], x] // Select[#, # =!= 0 &] &)*Table[(-1)^n*(2*n+1)!, {n, 0, max-1}] ) ; coes[[j+1 ;; -1]][[All, j+1]] (* _Jean-François Alcover_, May 14 2013 *)
%Y Cf. A060628 (3rd lower diagonal).
%K nonn
%O 0,2
%A _Simon Plouffe_
%E Typo in a(7) fixed by _Jean-François Alcover_, May 14 2013
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