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
Keywords
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.
Programs
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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 *)
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