OFFSET
0,2
LINKS
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) = (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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Typo in a(7) fixed by Jean-François Alcover, May 14 2013
STATUS
approved