A292761 Expansion of e.g.f. (tan x + sec x)^2*(E.g.f. for A000738).

0, 1, 7, 38, 201, 1115, 6626, 42517, 295107, 2211892, 17849935, 154550441, 1430572848, 14107448549, 147729473099, 1637748919090, 19167768256629, 236221157717491, 3058140944567938, 41499024082744529, 589093653165279255, 8731488105231566648, 134896745065585496747

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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 + 13/2) * n^(n + 5/2) / (sqrt(5) * Pi^(n + 5/2) * 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)^3 / Cos[x]^3, {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 02 2019 *)

Crossrefs

Cf. A000045, A000738, A292760.

Sequence in context: A099461 A104553 A027241 * A226200 A056197 A348457

Adjacent sequences: A292758 A292759 A292760 * A292762 A292763 A292764

Keyword

nonn

Author

N. J. A. Sloane, Sep 26 2017

Status

approved