%I #7 Jun 08 2019 08:28:58
%S 1,1,3,18,165,2000,29855,527632,10762857,248811264,6428081979,
%T 183537694208,5739195739277,195059957567488,7159662639822615,
%U 282252719348582400,11894243092571825745,533554809104057434112,25384473065818477067123,1276688324194885747474432
%N a(n) = n! * [x^n] exp(n*x)/cosh(x).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) ~ n^n / cosh(1). - _Vaclav Kotesovec_, Jun 08 2019
%t Table[n! SeriesCoefficient[Exp[n x]/Cosh[x], {x, 0, n}], {n, 0, 19}]
%t Table[2^n EulerE[n, (n + 1)/2], {n, 0, 19}]
%Y Cf. A000364, A062024, A119880, A119881, A155585, A302583, A302584, A302586, A302587.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 10 2018