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 A294642 #13 Oct 11 2018 17:34:23
%S A294642 1,1,6,45,456,5825,89896,1627437,33822944,793783233,20765009344,
%T A294642 599157626925,18904594000128,647524807918209,23929038677825152,
%U A294642 948995910652193325,40203601321988822528,1812025020244371552897,86577002960871477916672,4371100278517527047687213
%N A294642 a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*sqrt(2)*x)/(sqrt(2)*x).
%H A294642 G. C. Greubel, <a href="/A294642/b294642.txt">Table of n, a(n) for n = 0..250</a>
%F A294642 a(n) = [x^n] (1 - n*x - sqrt(1 - 2*n*x + (n^2 - 8)*x^2))/(4*x^2).
%F A294642 a(n) = [x^n] 1/(1 - n*x - 2*x^2/(1 - n*x - 2*x^2/(1 - n*x - 2*x^2/(1 - n*x - 2*x^2/(1 - ...))))), a continued fraction.
%F A294642 a(n) = Sum_{k=0..floor(n/2)} 2^k*n^(n-2*k)*binomial(n,2*k)*A000108(k).
%F A294642 a(n) = n^n*2F1(1/2-n/2,-n/2; 2; 8/n^2).
%F A294642 a(n) ~ c * n^n, where c = BesselI(1, 2*sqrt(2))/sqrt(2) = 2.3948330992734... - _Vaclav Kotesovec_, Nov 06 2017
%t A294642 Simplify[Table[n! SeriesCoefficient[Exp[n x] BesselI[1, 2 Sqrt[2] x]/(Sqrt[2] x), {x, 0, n}], {n, 0, 19}]]
%t A294642 Table[SeriesCoefficient[(1 - n x - Sqrt[1 - 2 n x + (n^2 - 8) x^2])/(4 x^2), {x, 0, n}], {n, 0, 19}]
%t A294642 Table[SeriesCoefficient[1/(1 - n x + ContinuedFractionK[-2 x^2, 1 - n x, {i, 1, n}]), {x, 0, n}], {n, 0, 19}]
%t A294642 Join[{1}, Table[Sum[2^k n^(n - 2 k) Binomial[n, 2 k] CatalanNumber[k], {k, 0, Floor[n/2]}], {n, 1, 19}]]
%t A294642 Join[{1}, Table[n^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {2}, 8/n^2], {n, 1, 19}]]
%Y A294642 Cf. A000108, A001003, A025235, A068764, A071356, A151374, A247496, A292716.
%K A294642 nonn
%O A294642 0,3
%A A294642 _Ilya Gutkovskiy_, Nov 05 2017