A336024 Expansion of e.g.f. (1 + sinh(x)) / cos(x).

1, 1, 1, 4, 5, 36, 61, 624, 1385, 18256, 50521, 814144, 2702765, 51475776, 199360981, 4381112064, 19391512145, 482962852096, 2404879675441, 66942218896384, 370371188237525, 11394877025289216, 69348874393137901, 2336793875186479104, 15514534163557086905

Offset: 0

Author

Ilya Gutkovskiy, Jul 05 2020

Keywords

• nonn

Crossrefs

Cf. A000111, A000364, A002084, A003701.

Programs

Mathematica

nmax = 24; CoefficientList[Series[(1 + Sinh[x])/Cos[x], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := If[EvenQ[n], Abs[EulerE[n]], Sum[Binomial[n, k] Abs[EulerE[k]], {k, 0, n}]]; Table[a[n], {n, 0, 24}]

Formula

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