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 A381860 #10 Mar 10 2025 10:37:18
%S A381860 1,4,12,55,327,2157,15141,110853,836790,6465309,50876776,406335099,
%T A381860 3285202335,26835060422,221128733649,1835973630276,15344202894457,
%U A381860 128983332603009,1089803313492966,9250137181234430,78837133437062307,674408139329393187,5788618956395607745
%N A381860 G.f. A(x) satisfies A(x) = (1 + x)^3 * C(x*A(x)), where C(x) is the g.f. of A000108.
%F A381860 a(n) = Sum_{k=0..n} binomial(3*k+1,k) * binomial(3*k+3,n-k)/(3*k+1).
%F A381860 D-finite with recurrence -2*n*(2*n+1)*a(n) +3*(n^2+13*n-6)*a(n-1) +3*(69*n^2-221*n+150)*a(n-2) +2*(397*n^2-2431*n+3471)*a(n-3) +6*(225*n^2-1953*n+4079)*a(n-4) +9*(135*n^2-1503*n+4084)*a(n-5) +9*(63*n^2-855*n+2860)*a(n-6) +12*(3*n-22)*(3*n-26)*a(n-7)=0. - _R. J. Mathar_, Mar 10 2025
%o A381860 (PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(3*k+3, n-k)/(3*k+1));
%Y A381860 Cf. A367640, A381787.
%Y A381860 Cf. A000108, A381882.
%K A381860 nonn
%O A381860 0,2
%A A381860 _Seiichi Manyama_, Mar 08 2025