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

0,3

Links

Table of n, a(n) for n=0..23.

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.

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

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 *)

Crossrefs

Cf. A000045, A000738.

Sequence in context: A323262 A295601 A301946 * A270322 A056884 A006749

Adjacent sequences: A292757 A292758 A292759 * A292761 A292762 A292763

Keyword

nonn

Author

N. J. A. Sloane, Sep 26 2017

Status

approved