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 A098461 #31 Apr 01 2024 13:02:40
%S A098461 1,1,6,42,456,6120,101520,1980720,44634240,1139080320,32488646400,
%T A098461 1023985670400,35345049062400,1325988036172800,53721616851302400,
%U A098461 2337607853957376000,108727934847307776000,5383304681800421376000,282682783375630589952000
%N A098461 Expansion of E.g.f.: 1/sqrt(1-2*x-3*x^2).
%H A098461 G. C. Greubel, <a href="/A098461/b098461.txt">Table of n, a(n) for n = 0..379</a>
%F A098461 a(n) = (n!/2^n)*A098453(n);
%F A098461 a(n) = (n!/2^n)*Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(2*(n-k), n)*3^k.
%F A098461 D-finite with recurrence: a(n) +(1-2n)*a(n-1) -3(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Dec 11 2011
%F A098461 a(n) = n! * A002426(n). - _Anton Zakharov_, Sep 14 2016
%t A098461 Table[(n!/2^n) Sum[Binomial[n, k] Binomial[2 (n - k), n] 3^k, {k, 0, Floor[n/2]}], {n, 0, 17}] (* _Michael De Vlieger_, Sep 14 2016 *)
%Y A098461 Cf. A012244, A098460, A002426.
%Y A098461 Main diagonal of A094796.
%K A098461 easy,nonn
%O A098461 0,3
%A A098461 _Paul Barry_, Sep 08 2004