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Expansion of e.g.f. (1 + sinh(x)) / cos(x).
0

%I #4 Jul 05 2020 07:29:28

%S 1,1,1,4,5,36,61,624,1385,18256,50521,814144,2702765,51475776,

%T 199360981,4381112064,19391512145,482962852096,2404879675441,

%U 66942218896384,370371188237525,11394877025289216,69348874393137901,2336793875186479104,15514534163557086905

%N Expansion of e.g.f. (1 + sinh(x)) / cos(x).

%F a(2*n) = A000364(n), a(2*n+1) = A002084(n).

%t nmax = 24; CoefficientList[Series[(1 + Sinh[x])/Cos[x], {x, 0, nmax}], x] Range[0, nmax]!

%t a[n_] := If[EvenQ[n], Abs[EulerE[n]], Sum[Binomial[n, k] Abs[EulerE[k]], {k, 0, n}]]; Table[a[n], {n, 0, 24}]

%Y Cf. A000111, A000364, A002084, A003701.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jul 05 2020