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 A293491 #6 Oct 16 2017 04:45:41
%S A293491 1,3,18,155,1734,23877,390804,7417377,160256070,3885021569,
%T A293491 104465601756,3086353547433,99399100528924,3466411543407555,
%U A293491 130151205663179112,5235127829223881895,224609180728848273990,10239557195235638377449,494317596005491398892620,25192788307121307053168673
%N A293491 a(n) = n! * [x^n] exp((n+2)*x)*BesselI(0,2*x).
%C A293491 The n-th term of the n-th binomial transform of A000984.
%H A293491 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A293491 a(n) = [x^n] 1/sqrt((1 - n*x)*(1 - (n + 4)*x)).
%F A293491 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2*k,k)*n^(n-k).
%F A293491 a(n) ~ exp(2) * BesselI(0,2) * n^n. - _Vaclav Kotesovec_, Oct 16 2017
%t A293491 Table[n! SeriesCoefficient[Exp[(n + 2) x] BesselI[0, 2 x], {x, 0, n}], {n, 0, 19}]
%t A293491 Table[SeriesCoefficient[1/Sqrt[(1 - n x) (1 - (n + 4) x)], {x, 0, n}], {n, 0, 19}]
%t A293491 Join[{1}, Table[Sum[Binomial[n, k] Binomial[2 k, k] n^(n - k), {k, 0, n}], {n, 1, 19}]]
%t A293491 Table[(n + 2)^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {1}, 4/(2 + n)^2], {n, 0, 19}]
%Y A293491 Cf. A000984, A026375, A081671, A098409, A098410, A104454, A186925, A292627, A292632.
%K A293491 nonn
%O A293491 0,2
%A A293491 _Ilya Gutkovskiy_, Oct 10 2017