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 A364825 #23 Aug 10 2023 04:49:02
%S A364825 1,2,18,222,3166,49098,804138,13686198,239671590,4290463698,
%T A364825 78160665666,1444298971662,27005948771886,510024567278234,
%U A364825 9714561608833242,186403770207998310,3599812021110287862,69914211761486437026,1364692279095996581490
%N A364825 G.f. satisfies A(x) = 1 - x*A(x)^3 * (1 - 3*A(x)).
%H A364825 Seiichi Manyama, <a href="/A364825/b364825.txt">Table of n, a(n) for n = 0..757</a>
%F A364825 a(n) = (-1)^n * Sum_{k=0..n} (-3)^k * binomial(n,k) * binomial(3*n+k+1,n) / (3*n+k+1).
%F A364825 a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(4*n-k,n-1-k) for n > 0.
%F A364825 a(n) = (1/n) * Sum_{k=1..n} 2^k * 3^(n-k) * binomial(n,k) * binomial(3*n,k-1) for n > 0.
%F A364825 D-finite with recurrence +2079*n*(3*n-1)*(3*n+1)*a(n) +(-347173*n^3 +395007*n^2 -41030*n -43092)*a(n-1) +18*(-59207*n^3 +325826*n^2 -590255*n +352406)*a(n-2) +3*(-3299*n^3 +35998*n^2 -125399*n +141144)*a(n-3) +9*(3*n-10)*(3*n-11) *(n-4)*a(n-4)=0. - _R. J. Mathar_, Aug 10 2023
%p A364825 A364825 := proc(n)
%p A364825 (-1)^n*add( (-3)^k*binomial(n,k) * binomial(3*n+k+1,n)/(3*n+k+1),k=0..n) ;
%p A364825 end proc:
%p A364825 seq(A364825(n),n=0..80); # _R. J. Mathar_, Aug 10 2023
%o A364825 (PARI) a(n) = (-1)^n*sum(k=0, n, (-3)^k*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
%Y A364825 Cf. A025192, A107841, A235347, A364826, A364827.
%Y A364825 Cf. A144097, A243659.
%K A364825 nonn
%O A364825 0,2
%A A364825 _Seiichi Manyama_, Aug 09 2023