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 A381861 #14 Mar 09 2025 09:55:26
%S A381861 1,5,32,231,1797,14715,125064,1093194,9766783,88793815,818832674,
%T A381861 7640868924,72014955566,684551660324,6555290711728,63179148757584,
%U A381861 612376024087047,5965515657187437,58375460484257734,573545171374958628,5655759227878768987,55957005428512022905
%N A381861 G.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * C(x), where C(x) is the g.f. of A000108.
%F A381861 a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(4*n-4*k+4,n-k)/(n+k+1).
%F A381861 a(n) = binomial(4 + 4*n, n)*hypergeom([-4/3-n, -2/3-n, -n, 1+n], [-3/4-n, -1/2-n, -1/4-n], 3^3/2^8)/(1 + n). - _Stefano Spezia_, Mar 09 2025
%o A381861 (PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+4, n-k)/(n+k+1));
%Y A381861 Cf. A000108, A127632, A153299.
%Y A381861 Cf. A381877.
%K A381861 nonn
%O A381861 0,2
%A A381861 _Seiichi Manyama_, Mar 08 2025