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 A378669 #13 Dec 04 2024 08:39:33
%S A378669 1,3,21,187,1878,20277,229806,2696523,32478204,399230972,4988220669,
%T A378669 63165060093,808828667104,10455471983550,136255868388684,
%U A378669 1788233397919211,23614059664575324,313531617379965156,4183068478829324388,56052027108881747724,754020313029799707018
%N A378669 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(4/3)/(1 - x*A(x)^(4/3)) )^3.
%F A378669 G.f.: exp( 3/4 * Sum_{k>=1} A378613(k) * x^k/k ).
%F A378669 G.f.: B(x)^3 where B(x) is the g.f. of A243667.
%F A378669 a(n) = 3 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(4*n+k+3,n)/(4*n+k+3).
%F A378669 a(n) = 3 * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n-1,n-k)/(4*n+k+3).
%F A378669 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 - x*A(x)^(4/3)) )^3.
%o A378669 (PARI) a(n) = 3*sum(k=0, n, 2^k*(-1)^(n-k)*binomial(n, k)*binomial(4*n+k+3, n)/(4*n+k+3));
%o A378669 (PARI) a(n, r=3, s=1, t=5, u=4) = 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 A378669 Cf. A243667, A378610, A378668.
%Y A378669 Cf. A378613.
%K A378669 nonn
%O A378669 0,2
%A A378669 _Seiichi Manyama_, Dec 02 2024