A242240 - OEIS

%I #11 Aug 15 2017 04:41:28

%S 0,1,0,0,0,12,0,0,0,3024,0,0,0,4390848,0,0,0,21224560896,0,0,0,

%T 257991277243392,0,0,0,6628234834692624384,0,0,0,

%U 319729080846260095008768,0,0,0,26571747463798134334265819136,0,0,0,3564202847752289659513902717468672,0,0,0

%N Expansion of Jacobi sn(x, 1/2) / cd(x, 1/2).

%F a(n) = |A104203(n)|.

%F E.g.f.: sn(x, 1/2) / cd(x, 1/2).

%F E.g.f. A(x) satisfies A(x)^2 = sinh(2 * Integral A(x) dx). - _Michael Somos_, Jun 17 2017

%e G.f. = x + 12*x^5 + 3024*x^9 + 4390848*x^13 + 21224560896*x^17 + ...

%t a[ n_] := If[ n<0, 0, n! SeriesCoefficient[ JacobiSN[x, 1/2] / JacobiCD[x, 1/2], {x, 0, n}]];

%o (PARI) {a(n) = if( n<0, 0, n! * polcoeff( serreverse( intformal( (1 + x^4 + x * O(x^n))^(-1/2))), n))};

%Y Cf. A104203.

%K nonn

%O 0,6

%A _Michael Somos_, May 09 2014