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 A378801 #17 Dec 09 2024 11:02:26
%S A378801 1,3,6,16,48,153,511,1761,6219,22383,81804,302766,1132475,4274166,
%T A378801 16256685,62249167,239772510,928398831,3611539758,14107963848,
%U A378801 55318781982,217652858539,859027927911,3400055112777,13492710661658,53673238384560,213984657134418
%N A378801 G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(2/3)) )^3.
%F A378801 G.f. A(x) satisfies A(x) = 1 + x * (1 + A(x)^(1/3) + A(x)^(5/3)).
%F A378801 G.f.: A(x) = (1 + x*B(x))^3 where B(x) is the g.f. of A161634.
%F A378801 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).
%o A378801 (PARI) a(n, r=3, s=1, 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 A378801 Cf. A161634, A365118.
%Y A378801 Cf. A005554, A378858.
%K A378801 nonn
%O A378801 0,2
%A A378801 _Seiichi Manyama_, Dec 09 2024