A242240 Expansion of Jacobi sn(x, 1/2) / cd(x, 1/2).

0, 1, 0, 0, 0, 12, 0, 0, 0, 3024, 0, 0, 0, 4390848, 0, 0, 0, 21224560896, 0, 0, 0, 257991277243392, 0, 0, 0, 6628234834692624384, 0, 0, 0, 319729080846260095008768, 0, 0, 0, 26571747463798134334265819136, 0, 0, 0, 3564202847752289659513902717468672, 0, 0, 0

Offset: 0

Author

Michael Somos, May 09 2014

Keywords

• nonn

Examples

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

Crossrefs

Cf. A104203.

Programs

Mathematica

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

PARI

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

Formula

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

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

E.g.f. A(x) satisfies A(x)^2 = sinh(2 * Integral A(x) dx). - Michael Somos, Jun 17 2017