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 A378733 #11 Dec 15 2024 09:08:15
%S A378733 1,1,4,18,96,551,3332,20906,134820,888151,5951096,40432550,277892604,
%T A378733 1928668910,13497833600,95150192558,674993798716,4815149310441,
%U A378733 34519885929860,248571425473698,1797058507267104,13038781500215352,94914559729835580,692987915940266152
%N A378733 G.f. A(x) satisfies A(x) = 1 + x / (1 - x*A(x)^2)^4.
%F A378733 G.f.: A(x) = sqrt(B(x)) where B(x) is the g.f. of A365123.
%F A378733 If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).
%p A378733 A378733 := proc(n)
%p A378733 add(binomial(2*(n-k)+1, k)*binomial(n+3*k-1, n-k)/(2*(n-k)+1),k=0..n) ;
%p A378733 end proc:
%p A378733 seq(A378733(n),n=0..80) ; # _R. J. Mathar_, Dec 15 2024
%o A378733 (PARI) a(n, r=1, s=4, t=0, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y A378733 Cf. A001764, A161634, A367236.
%Y A378733 Cf. A365123.
%K A378733 nonn
%O A378733 0,3
%A A378733 _Seiichi Manyama_, Dec 06 2024