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 A262910 #22 Sep 29 2022 16:08:27
%S A262910 1,2,10,59,366,2337,15205,100235,667222,4474733,30188335,204646532,
%T A262910 1392850785,9511878729,65144238981,447263887479,3077459618886,
%U A262910 21215286546705,146500755609415,1013180180867125,7016536189029551,48650933146617728,337709155342663620
%N A262910 a(n) = Sum_{k=0..n} binomial(k+n-1,k)*binomial(k+n,2*k).
%H A262910 Alois P. Heinz, <a href="/A262910/b262910.txt">Table of n, a(n) for n = 0..1176</a>
%F A262910 G.f.: A(x) = x*B'(x)/B(x), where B(x)/x is g.f. of A007863.
%F A262910 Recurrence: 5*(n-1)*n*(35*n^2 - 143*n + 138)*a(n) = 2*(n-1)*(630*n^3 - 2889*n^2 + 3746*n - 1200)*a(n-1) - 2*(70*n^4 - 426*n^3 + 811*n^2 - 589*n + 150)*a(n-2) + 2*(n-3)*(2*n - 3)*(35*n^2 - 73*n + 30)*a(n-3). - _Vaclav Kotesovec_, Oct 04 2015
%F A262910 a(n) = hypergeom([-n, n, n+1], [1/2, 1], -1/4). - _Peter Luschny_, Oct 08 2015
%F A262910 a(n) = A155112(2n,n). - _Alois P. Heinz_, Sep 29 2022
%p A262910 a := n -> hypergeom([-n, n, n+1], [1/2, 1], -1/4):
%p A262910 seq(round(evalf(a(n), 32)), n=0..21); # _Peter Luschny_, Oct 08 2015
%t A262910 Table[Sum[Binomial[k+n-1,k]*Binomial[k+n,2*k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Oct 04 2015 *)
%o A262910 (Maxima)
%o A262910 B(x):=sum(sum(binomial(i+n-1,i)*binomial(i+n,2*i+1),i,0,n-1)/n*x^n,n,1,30);
%o A262910 taylor(x*diff(B(x),x)/B(x),x,0,20);
%o A262910 (PARI) a(n) = sum(k=0, n, binomial(k+n-1,k)*binomial(k+n,2*k));
%o A262910 vector(50, n, a(n-1)) \\ _Altug Alkan_, Oct 04 2015
%Y A262910 Cf. A007863, A155112.
%K A262910 nonn
%O A262910 0,2
%A A262910 _Vladimir Kruchinin_, Oct 04 2015