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 A073156 #10 Dec 07 2024 10:41:35
%S A073156 1,2,9,36,156,698,3210,15080,72060,349184,1711869,8475494,42318018,
%T A073156 212843826,1077391794,5484472880,28058940086,144195777552,
%U A073156 744017466318,3852968380624,20019113126120,104329129258596,545214946753377
%N A073156 Main diagonal sequence of triangle A073153.
%F A073156 Convolution of sequence A073155: a(n) = Sum_{k=0..n} A073155(k) * A073155(n-k).
%F A073156 G.f.: 1/4*(1-(1-4*x*(1+x)^2)^(1/2))^2/x^2/(1+x)^4. - _Vladeta Jovovic_, Oct 10 2003
%F A073156 From _Seiichi Manyama_, Dec 07 2024: (Start)
%F A073156 G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x)^2 * A(x) )^2.
%F A073156 a(n) = Sum_{k=0..n} binomial(2*k+2,k) * binomial(2*k,n-k)/(k+1). (End)
%o A073156 (PARI) a(n, r=2, s=2, t=2, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r)); \\ _Seiichi Manyama_, Dec 07 2024
%Y A073156 Cf. A073153, A073155, A073157.
%K A073156 easy,nonn
%O A073156 0,2
%A A073156 _Paul D. Hanna_, Jul 29 2002
%E A073156 More terms from _Vladeta Jovovic_, Oct 10 2003