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 A378670 #17 Dec 04 2024 08:39:29
%S A378670 1,2,11,78,627,5432,49464,466726,4522871,44747874,450127999,
%T A378670 4589821576,47333631828,492836382192,5173697858508,54700317431958,
%U A378670 581946708333055,6225343630256678,66921440314606905,722546760572660030,7832054418695360555,85198490262065775840
%N A378670 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(3/2)/(1 - x*A(x)^(3/2)) )^2.
%F A378670 G.f.: exp( 2/3 * Sum_{k>=1} A378612(k) * x^k/k ).
%F A378670 G.f.: B(x)^2 where B(x) is the g.f. of A243659.
%F A378670 a(n) = 2 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(3*n+k+2,n)/(3*n+k+2).
%F A378670 a(n) = 2 * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n-1,n-k)/(3*n+k+2).
%F A378670 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^2/(1 - x*A(x)^(3/2)) )^2.
%o A378670 (PARI) a(n) = 2*sum(k=0, n, 2^k*(-1)^(n-k)*binomial(n, k)*binomial(3*n+k+2, n)/(3*n+k+2));
%o A378670 (PARI) a(n, r=2, s=1, t=4, u=3) = 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 A378670 Cf. A243659, A369012.
%Y A378670 Cf. A010683, A211789, A378668.
%Y A378670 Cf. A378612.
%K A378670 nonn
%O A378670 0,2
%A A378670 _Seiichi Manyama_, Dec 02 2024