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a(n) = n! * [x^n] exp(n*x)/cosh(x).
8

%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