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%I #4 Dec 26 2017 18:05:51
%S 1,0,3,15,224,4545,126753,4626076,213703095,12167727543,835893746300,
%T 68091766034061,6483302813035857,712860388963255000,
%U 89585739948801890619,12753524767335858733935,2040804997678590563632568,364567987004433619078313961
%N Expansion of e.g.f. cosh(x*tan(x/2)) (even powers only).
%F a(n) = (2*n)! * [x^(2*n)] cosh(x*tan(x/2)).
%e 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! + ...
%t 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}]
%Y Cf. A001469, A003711, A009166, A110501, A296839, A296841, A296842, A296853, A296854.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 21 2017
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