A292760 Expansion of e.g.f. (tan x + sec x)*(E.g.f. for A000738).

0, 1, 5, 20, 83, 375, 1860, 10205, 61701, 409240, 2959775, 23209055, 196266104, 1781241825, 17274311925, 178313963300, 1952338563867, 22601633554855, 275867860584620, 3540918330014765, 47682832410552965, 672211363480355880, 9901286664553498695, 152101199645144064575

Offset: 0

Author

N. J. A. Sloane, Sep 26 2017

Keywords

• nonn

Links

• C. K. Cook, M. R. Bacon, and R. A. Hillman, Higher-order Boustrophedon transforms for certain well-known sequences, Fib. Q., 55(3) (2017), 201-208.

Crossrefs

Cf. A000045, A000738.

Programs

Mathematica

nmax = 20; FullSimplify[CoefficientList[Series[2/Sqrt[5] * E^(x/2) * Sinh[Sqrt[5]*x/2] * (Sin[x]+1)^2 / Cos[x]^2, {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 02 2019 *)

Formula

a(n) ~ sinh(sqrt(5)*Pi/4) * 2^(n + 11/2) * n^(n + 3/2) / (sqrt(5) * Pi^(n + 3/2) * exp(n - Pi/4)). - Vaclav Kotesovec, Jun 02 2019