A296856 Expansion of e.g.f. cosh(x*tan(x/2)) (even powers only).

1, 0, 3, 15, 224, 4545, 126753, 4626076, 213703095, 12167727543, 835893746300, 68091766034061, 6483302813035857, 712860388963255000, 89585739948801890619, 12753524767335858733935, 2040804997678590563632568, 364567987004433619078313961

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• nonn

Examples

			cosh(x*tan(x/2)) = 1 + 3*x^4/4! + 15*x^6/6! + 224*x^8/8! + 4545*x^10/10! + 126753*x^12/12! + ...
		

Crossrefs

Cf. A001469, A003711, A009166, A110501, A296839, A296841, A296842, A296853, A296854.

Programs

Mathematica

nmax = 17; Table[(CoefficientList[Series[Cosh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Formula

a(n) = (2*n)! * [x^(2*n)] cosh(x*tan(x/2)).