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 A137637 #6 Nov 25 2023 08:41:07
%S A137637 1,6,32,170,899,4764,25318,134964,721562,3868024,20785035,111931154,
%T A137637 603938905,3264309644,17671408012,95800342628,520022296700,
%U A137637 2826089180652,15374990077568,83727902852188,456370687687082
%N A137637 a(n) = Sum_{k=0..n} C(2k+2,k)*C(2k+2,n-k) ; equals row 2 of square array A137634 ; also equals the convolution of A137635 and the self-convolution of A073157.
%H A137637 Seiichi Manyama, <a href="/A137637/b137637.txt">Table of n, a(n) for n = 0..1000</a>
%F A137637 G.f.: A(x) = R(x)*G(x)^2, where R(x) = 1/sqrt(1-4*x*(1+x)^2) is the g.f. of A137635 and G(x) = (1-sqrt(1-4*x*(1+x)^2))/(2*x*(1+x)) is the g.f. of A073157.
%o A137637 (PARI) {a(n)=sum(k=0,n,binomial(2*k+2,k)*binomial(2*k+2,n-k))} /* Using the g.f.: */ {a(n)=local(R=1/sqrt(1-4*x*(1+x +x*O(x^n))^2), G=(1-sqrt(1-4*x*(1+x)^2+x^2*O(x^n)))/(2*x*(1+x+x*O(x^n)))); polcoeff(R*G^2,n,x)}
%Y A137637 Cf. A137634, A137635, A137636, A137638, A073157.
%K A137637 nonn
%O A137637 0,2
%A A137637 _Paul D. Hanna_, Jan 31 2008