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%I #7 Jan 19 2019 20:23:09
%S 2,1,1,1,8,1,1,60,60,1,1,472,1824,472,1,1,3944,46576,46576,3944,1,1,
%T 34236,1129968,3077120,1129968,34236,1,1,303028,27126048,171931904,
%U 171931904,27126048,303028,1,1,2706800,653677408,8874639488,19720976896
%N Triangle T(n,m) of the expansion coefficients of JacobiCN(x,y) + JacobiDN(x,y) = Sum_{n>=0} Sum_{k=0..n} (-1)^n*T(n,m)*x^(2*n)*y^(2*m)/(2*n)!.
%C Row sums are 2*A000364(n).
%C Since the coefficients of JacobiCN are in A060627 and the coefficients of JacobiDN are obtained by row-reversal of A060627, this triangle here is a symmetrized variant, adding A060627 and its mirrored version.
%e 2;
%e 1, 1;
%e 1, 8, 1;
%e 1, 60, 60, 1;
%e 1, 472, 1824, 472, 1;
%e 1, 3944, 46576, 46576, 3944, 1;
%e 1, 34236, 1129968, 3077120, 1129968, 34236, 1;
%e 1, 303028, 27126048, 171931904, 171931904, 27126048, 303028, 1;
%e 1, 2706800, 653677408, 8874639488, 19720976896, 8874639488, 653677408, 2706800, 1;
%e 1, 24279312, 15877769376, 440712200064, 1948265426688, 1948265426688, 440712200064, 15877769376, 24279312, 1;
%e 1, 218186164, 388726995744, 21489645169920, 176743676925696, 343497841920000, 176743676925696, 21489645169920, 388726995744, 218186164, 1;
%p A171660 := proc(n,m) JacobiCN(z,k) +JacobiDN(z,k) ; coeftayl(%,z=0,2*n) ; (-1)^n*coeftayl(%,k=0,2*m)*(2*n)! ; end proc: # _R. J. Mathar_, Jan 30 2011
%t p[t_] = JacobiCN[t, x] + JacobiDN[t, x]
%t a = Table[ CoefficientList[FullSimplify[ExpandAll[(-1)^Floor[n/2]*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 20, 2}]
%t Flatten[a]
%Y Cf. A060627.
%K nonn,tabl
%O 0,1
%A _Roger L. Bagula_, Dec 14 2009
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