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 A378952 #11 Dec 12 2024 09:25:00
%S A378952 1,3,18,139,1218,11511,114398,1178421,12469626,134734092,1480317468,
%T A378952 16487870031,185744716414,2112756042468,24230663513604,
%U A378952 279889210974003,3253295301115290,38023971948455859,446603044829013514,5268557500949993964,62398899992129490756
%N A378952 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^2/(1 + x*A(x)^(4/3)) )^3.
%F A378952 G.f. A(x) satisfies:
%F A378952 (1) A(x) = 1/( 1 - x*A(x)^(5/3)/(1 + x*A(x)^(4/3)) )^3.
%F A378952 (2) A(x) = 1 + x * A(x)^(4/3) * (1 + A(x)^(2/3) + A(x)^(4/3)).
%F A378952 (3) A(x) = B(x)^3 where B(x) is the g.f. of A364765.
%F A378952 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(s*k,n-k)/(t*k+u*(n-k)+r).
%o A378952 (PARI) a(n, r=3, s=-1, t=6, u=4) = 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 A378952 Cf. A371724, A378951.
%Y A378952 Cf. A364765, A378954.
%Y A378952 Cf. A378891.
%K A378952 nonn
%O A378952 0,2
%A A378952 _Seiichi Manyama_, Dec 11 2024