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 A381826 #9 Mar 10 2025 10:41:50
%S A381826 1,2,8,41,241,1545,10503,74429,543833,4067510,30985633,239560975,
%T A381826 1874831287,14823253892,118222204539,949963236834,7683289712433,
%U A381826 62499664522578,510992689465500,4196824203859773,34609480384100715,286461380785102398,2378954616256505177
%N A381826 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^2), where C(x) is the g.f. of A000108.
%F A381826 a(n) = (1/(2*n+1)) * Sum_{k=0..n} binomial(2*n+1,k) * binomial(3*n-3*k,n-k).
%F A381826 D-finite with recurrence 12*n*(3*n+2)*(2*n+1)*(3*n+1)*a(n) +2*(-2365*n^4+2754*n^3-1799*n^2+834*n-144)*a(n-1) +2*(20215*n^4-89442*n^3+158117*n^2-135942*n+47592)*a(n-2) +(-181487*n^4+1469774*n^3-4524589*n^2+6309094*n-3370512)*a(n-3) +124*(n-3)*(2*n-7)*(1797*n^2-9448*n+12568)*a(n-4) -119164*(2*n-7)*(2*n-9)*(n-3)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Mar 10 2025
%o A381826 (PARI) a(n) = sum(k=0, n, binomial(2*n+1, k)*binomial(3*n-3*k, n-k))/(2*n+1);
%Y A381826 Cf. A014137, A129442, A381827.
%Y A381826 Cf. A000108.
%K A381826 nonn
%O A381826 0,2
%A A381826 _Seiichi Manyama_, Mar 08 2025