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 A378951 #11 Dec 12 2024 09:24:56
%S A378951 1,3,15,94,663,5025,39970,329145,2782095,23999078,210427869,
%T A378951 1869908364,16802935370,152425394958,1393972037301,12838326815582,
%U A378951 118970843349711,1108503805898190,10378559702646846,97593299922016224,921294705307189029
%N A378951 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 + x*A(x)) )^3.
%F A378951 G.f. A(x) satisfies:
%F A378951 (1) A(x) = 1/( 1 - x*A(x)^(4/3)/(1 + x*A(x)) )^3.
%F A378951 (2) A(x) = 1 + x * A(x) * (1 + A(x)^(2/3) + A(x)^(4/3)).
%F A378951 (3) A(x) = B(x)^3 where B(x) is the g.f. of A271469.
%F A378951 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 A378951 (PARI) a(n, r=3, s=-1, t=5, u=3) = 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 A378951 Cf. A371724, A378952.
%Y A378951 Cf. A271469, A370474.
%Y A378951 Cf. A378891.
%K A378951 nonn
%O A378951 0,2
%A A378951 _Seiichi Manyama_, Dec 11 2024