cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A292761 #16 Jan 05 2025 19:51:41
%S A292761 0,1,7,38,201,1115,6626,42517,295107,2211892,17849935,154550441,
%T A292761 1430572848,14107448549,147729473099,1637748919090,19167768256629,
%U A292761 236221157717491,3058140944567938,41499024082744529,589093653165279255,8731488105231566648,134896745065585496747
%N A292761 Expansion of e.g.f. (tan x + sec x)^2*(E.g.f. for A000738).
%H A292761 C. K. Cook, M. R. Bacon, and R. A. Hillman, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/55-3/CookBaconHillman01222017.pdf">Higher-order Boustrophedon transforms for certain well-known sequences</a>, Fib. Q., 55(3) (2017), 201-208.
%F A292761 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
%t A292761 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 *)
%Y A292761 Cf. A000045, A000738, A292760.
%K A292761 nonn
%O A292761 0,3
%A A292761 _N. J. A. Sloane_, Sep 26 2017