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 A378919 #6 Dec 11 2024 05:36:28
%S A378919 1,1,5,39,355,3532,37206,407861,4604493,53169811,625067441,7456004083,
%T A378919 90015754691,1097834790182,13505674728174,167395320811562,
%U A378919 2088350145491232,26203315734195937,330460721192844017,4186559092558049570,53255890990455126082,679954025388880445771
%N A378919 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)).
%F A378919 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^5/(1 + x*A(x))).
%F A378919 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 A378919 (PARI) a(n, r=1, s=-1, t=6, u=1) = 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 A378919 Cf. A002294, A349362, A364765, A365218, A378892, A378920.
%Y A378919 Cf. A106228, A364758, A364759.
%K A378919 nonn
%O A378919 0,3
%A A378919 _Seiichi Manyama_, Dec 11 2024