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.
%I A294222 #6 Feb 16 2025 08:33:51
%S A294222 1,1,4,14,69,372,2320,15913,119938,978456,8586177,80456488,800905726,
%T A294222 8429875989,93453556378,1087491751050,13244265431889,168370713583760,
%U A294222 2229127899764052,30671277674880073,437770190804865414,6470590710038358164,98891186448861721537,1560548838446810788940,25394750159240696915562
%N A294222 Exponential transform of the Lucas numbers (A000204).
%H A294222 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A294222 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A294222 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A294222 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialTransform.html">Exponential Transform</a>
%H A294222 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>
%F A294222 E.g.f.: exp(2*exp(x/2)*cosh(sqrt(5)*x/2) - 2).
%e A294222 E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 14*x^3/3! + 69*x^4/4! + 372*x^5/5! + 2320*x^6/6! + ...
%t A294222 Range[0, 24]! CoefficientList[Series[Exp[2 Exp[x/2] Cosh[Sqrt[5] x/2] - 2], {x, 0, 24}], x]
%t A294222 a[n_] := a[n] = Sum[a[n - k] Binomial[n - 1, k - 1] LucasL[k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]
%Y A294222 Cf. A000204, A256180, A279271.
%K A294222 nonn
%O A294222 0,3
%A A294222 _Ilya Gutkovskiy_, Oct 25 2017