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 A381772 #12 Mar 07 2025 10:48:52
%S A381772 1,2,11,83,727,6940,70058,735502,7949031,87851819,988307647,
%T A381772 11279719247,130286197186,1520108988221,17889102534329,
%U A381772 212095541328931,2531001870925559,30376237591559863,366417240105654587,4440000077166319993,54020150448778625847,659665548217188211288
%N A381772 Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^2 ) )^(1/2), where C(x) is the g.f. of A000108.
%F A381772 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * C(x*A(x)^2).
%F A381772 a(n) = Sum_{k=0..n} binomial(2*n+2*k+1,k) * binomial(2*n+1,n-k)/(2*n+2*k+1).
%o A381772 (PARI) my(N=30, x='x+O('x^N)); Vec((serreverse(x/((1+x)*(1-sqrt(1-4*x))/(2*x))^2)/x)^(1/2))
%Y A381772 Cf. A054727, A060941, A381773, A381774, A381775.
%Y A381772 Cf. A007852, A069271, A381780.
%Y A381772 Cf. A000108, A274052.
%K A381772 nonn
%O A381772 0,2
%A A381772 _Seiichi Manyama_, Mar 07 2025