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 A378786 #10 Dec 07 2024 10:41:39
%S A378786 1,1,6,39,296,2435,21138,190603,1767968,16761424,161697576,1582171216,
%T A378786 15664531716,156637712953,1579664567130,16048129755157,
%U A378786 164085811289360,1687224436103842,17436287104620980,181001686332329224,1886522317836670988,19734386503541838083
%N A378786 G.f. A(x) satisfies A(x) = 1 + x * (1+x)^2 * A(x)^4.
%F A378786 a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(2*k,n-k)/(4*k+1) = Sum_{k=0..n} binomial(2*k,n-k) * A002293(k).
%o A378786 (PARI) a(n, r=1, s=2, t=4, 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));
%Y A378786 Cf. A365178, A366216, A366272.
%Y A378786 Cf. A002478, A073155, A366221.
%Y A378786 Cf. A002293.
%K A378786 nonn
%O A378786 0,3
%A A378786 _Seiichi Manyama_, Dec 07 2024