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 A364431 #10 Jul 25 2023 07:31:36
%S A364431 1,3,27,351,5319,87885,1535517,27898101,521740197,9977087439,
%T A364431 194191054263,3834392341779,76619557946475,1546479815079321,
%U A364431 31482877148802873,645689728734541929,13328555370318744777,276704344407952939131,5773556701375333682355
%N A364431 G.f. satisfies A(x) = 1 + x*A(x)*(1 + 2*A(x)^3).
%F A364431 a(n) = Sum_{k=0..n} 2^k * binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1).
%F A364431 D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-458*n^3 +201*n^2 +401*n -216)*a(n-1) +3*(-1105*n^3 +6549*n^2 -11384*n +5796)*a(n-2) +18*(-262*n^3 +2877*n^2 -10295*n +12006)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) -81*(10*n-51) *(n-4)*(n-5)*a(n-5) +243*(n-5)*(n-6) *(n-4)*a(n-6)=0. - _R. J. Mathar_, Jul 25 2023
%p A364431 A364431 := proc(n)
%p A364431 add(2^k* binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1),k=0..n) ;
%p A364431 end proc:
%p A364431 seq(A364431(n),n=0..70); # _R. J. Mathar_, Jul 25 2023
%o A364431 (PARI) a(n) = sum(k=0, n, 2^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));
%Y A364431 Cf. A103210, A348912.
%Y A364431 Cf. A364430, A364432.
%K A364431 nonn
%O A364431 0,2
%A A364431 _Seiichi Manyama_, Jul 24 2023