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 A378690 #9 Dec 04 2024 09:11:32
%S A378690 1,2,17,190,2438,33938,498413,7602010,119261202,1912171310,
%T A378690 31194947785,516153663072,8641160417191,146105874059670,
%U A378690 2491396820758004,42795782630083868,739842609794223330,12862556429464405500,224744883747568868574,3944534317072930309360
%N A378690 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/2)/(1 - x*A(x)) )^2.
%F A378690 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3/(1 - x*A(x)) )^2.
%F A378690 G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A378688.
%F A378690 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 A378690 (PARI) a(n, r=2, s=1, t=7, 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 A378690 Cf. A378686, A378692, A378693.
%Y A378690 Cf. A378688.
%K A378690 nonn
%O A378690 0,2
%A A378690 _Seiichi Manyama_, Dec 04 2024