cp's OEIS Frontend

A376490 G.f. satisfies A(x) = 1 / (1 - x^3*A(x)^3 / (1 - x)).

%I A376490 #11 Sep 26 2024 04:36:59
%S A376490 1,0,0,1,1,1,5,9,13,39,87,157,389,923,1899,4426,10582,23414,54022,
%T A376490 128643,295735,686881,1631513,3825456,8974024,21330400,50550032,
%U A376490 119644037,285176865,680215735,1621245503,3878312658,9293056066,22267588692,53463982624
%N A376490 G.f. satisfies A(x) = 1 / (1 - x^3*A(x)^3 / (1 - x)).
%F A376490 a(n) = Sum_{k=0..floor(n/3)} binomial(4*k,k) * binomial(n-2*k-1,n-3*k) / (3*k+1).
%F A376490 D-finite with recurrence 243*n*(n-1)*(n+1)*a(n) -81*n*(n-1)*(16*n-29)*a(n-1) +27*(106*n-285)*(n-1)*(n-2)*a(n-2) +9*(-628*n^3+4365*n^2-10585*n+8778)*a(n-3) +3*(4057*n^3-33849*n^2+94446*n-89368)*a(n-4) +2*(-8954*n^3+98325*n^2-354169*n+419010)*a(n-5) +12*(1225*n^3-17314*n^2+80552*n-123168)*a(n-6) -384*(2*n-13)*(8*n^2-88*n+239)*a(n-7) +256*(2*n-15)*(n-7)*(2*n-13)*a(n-8)=0. - _R. J. Mathar_, Sep 26 2024
%p A376490 A376490 := proc(n)
%p A376490     add(binomial(4*k,k)*binomial(n-2*k-1,n-3*k)/(3*k+1),k=0..floor(n/3)) ;
%p A376490 end proc:
%p A376490 seq(A376490(n),n=0..70) ; # _R. J. Mathar_, Sep 26 2024
%o A376490 (PARI) a(n) = sum(k=0, n\3, binomial(4*k, k)*binomial(n-2*k-1, n-3*k)/(3*k+1));
%Y A376490 Cf. A002212, A376489, A376491.
%K A376490 nonn
%O A376490 0,7
%A A376490 _Seiichi Manyama_, Sep 25 2024