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 A294573 #18 Nov 13 2017 06:32:06
%S A294573 1,2,10,76,777,9996,155139,2821400,58856963,1385621260,36343079188,
%T A294573 1051024082472,33226817252215,1140040324751160,42193259673938754,
%U A294573 1675570154136359472,71069261432474378715,3206616936773061141900,153358034674756782660342,7749560706936442485607560
%N A294573 a(n) = n! * [x^n] exp((n+1)*x)*BesselI(1,2*x)/x.
%C A294573 The n-th term of the n-th binomial transform of A001006.
%H A294573 Robert Israel, <a href="/A294573/b294573.txt">Table of n, a(n) for n = 0..300</a>
%H A294573 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A294573 a(n) = [x^n] (1 - (n + 1)*x - sqrt((1 - (n - 1)*x)*(1 - (n + 3)*x)))/(2*x^2).
%F A294573 a(n) ~ exp(1) * BesselI(1,2) * n^n. - _Vaclav Kotesovec_, Nov 13 2017
%p A294573 S:= series(exp((n+1)*x)*BesselI(1,2*x)/x, x, 102):
%p A294573 seq(simplify(n!*coeff(S,x,n)),n=0..100); # _Robert Israel_, Nov 03 2017
%t A294573 Table[n! SeriesCoefficient[Exp[(n + 1) x] BesselI[1, 2 x]/x, {x, 0, n}], {n, 0, 19}]
%t A294573 Table[SeriesCoefficient[(1 - (n + 1) x - Sqrt[(1 - (n - 1) x) (1 - (n + 3) x)])/(2 x^2), {x, 0, n}], {n, 0, 19}]
%t A294573 Table[(n + 1)^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {2}, 4/(n + 1)^2], {n, 0, 19}]
%Y A294573 Diagonal of A247495.
%Y A294573 Cf. A001006, A247496.
%K A294573 nonn
%O A294573 0,2
%A A294573 _Ilya Gutkovskiy_, Nov 02 2017