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 A381876 #10 Mar 09 2025 09:55:42
%S A381876 1,4,23,156,1167,9311,77710,670294,5928183,53467931,489904745,
%T A381876 4547296624,42667426369,404044679434,3856480309376,37062228265769,
%U A381876 358330619946164,3482936427997599,34014454418349579,333598711996924548,3284326412065118717,32446900771699499147
%N A381876 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.
%F A381876 a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(4*n-4*k+2,n-k)/(n+k+1).
%F A381876 a(n) = binomial(2 + 4*n, n)*hypergeom([-2/3-n, -1/3-n, -n, 1+n], [-1/2-n, -1/4-n, 1/4-n], 3^3/2^8)/(1 + n). - _Stefano Spezia_, Mar 09 2025
%o A381876 (PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+2, n-k)/(n+k+1));
%Y A381876 Cf. A129442, A381875, A381877.
%Y A381876 Cf. A000108, A381880.
%K A381876 nonn
%O A381876 0,2
%A A381876 _Seiichi Manyama_, Mar 09 2025