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 A381909 #12 Mar 10 2025 07:01:08
%S A381909 1,3,16,121,1117,11569,128648,1500054,18091859,223794730,2823369749,
%T A381909 36185653049,469808971400,6165903108879,81667617713170,
%U A381909 1090234962290114,14654059445570507,198151602861222385,2693625234657193038,36789566028850640226,504600217464088999466
%N A381909 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A002293.
%F A381909 G.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * B(x*A(x)).
%F A381909 a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(2*n+2,n-k)/(n+4*k+1).
%F A381909 a(n) = binomial(2*(1 + n), n)*hypergeom([(1+n)/4, (2+n)/4, (3+n)/4, (4+n)/4, -n], [(2+n)/3, (3+n)/3, (4+n)/3, 3+n], -2^8/3^3)/(1 + n). - _Stefano Spezia_, Mar 10 2025
%o A381909 (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(2*n+2, n-k)/(n+4*k+1));
%Y A381909 Cf. A381908, A381910.
%Y A381909 Cf. A002293.
%K A381909 nonn
%O A381909 0,2
%A A381909 _Seiichi Manyama_, Mar 10 2025