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 A381881 #11 Mar 09 2025 12:26:20
%S A381881 1,3,14,82,547,3958,30249,240362,1966235,16449495,140093989,
%T A381881 1210575512,10587490383,93540456103,833619150838,7484887130882,
%U A381881 67645312129491,614872423359187,5617522739173495,51556112664387720,475105557839611760,4394434006611790855
%N A381881 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * C(x)) ), where C(x) is the g.f. of A000108.
%F A381881 G.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * C(x*A(x)).
%F A381881 a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(2*n+2,n-k)/(n+2*k+1).
%F A381881 a(n) = binomial(2*(1 + n), n)*hypergeom([(1+n)/2, 1+n/2, -n], [2 + n, 3 + n], -4)/(1 + n). - _Stefano Spezia_, Mar 09 2025
%o A381881 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1-sqrt(1-4*x))/(2*x)))/x)
%Y A381881 Cf. A054727, A381882.
%Y A381881 Cf. A000108, A381879.
%K A381881 nonn
%O A381881 0,2
%A A381881 _Seiichi Manyama_, Mar 09 2025