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 A379080 #10 Dec 15 2024 06:41:31
%S A379080 1,2,7,32,163,886,5039,29616,178446,1096356,6842452,43259122,
%T A379080 276462247,1783114592,11591769207,75874998822,499643588823,
%U A379080 3307746965238,22001986381873,146972401234478,985535271867577,6631547191254298,44763982636889092,303037237861086682
%N A379080 Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^2)^2 ).
%F A379080 G.f. A(x) satisfies:
%F A379080 (1) A(x) = exp( Sum_{k>=1} A379084(k) * x^k/k ).
%F A379080 (2) A(x) = ( (1 + x*A(x)) * (1 + x^2*A(x)^(5/2)) )^2.
%F A379080 (3) A(x) = B(x)^2 where B(x) is the g.f. of A200719.
%F A379080 a(n) = (1/(n+1)) * [x^n] 1/( 1/(1 + x) - x^2 )^(2*(n+1)).
%F A379080 a(n) = 2 * Sum_{k=0..floor(n/2)} binomial(2*n+k+2,k) * binomial(2*n+k+2,n-2*k)/(2*n+k+2) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(2*n+k+2,n-2*k).
%o A379080 (PARI) a(n) = 2*sum(k=0, n\2, binomial(2*n+k+2, k)*binomial(2*n+k+2, n-2*k)/(2*n+k+2));
%Y A379080 Cf. A181734, A379081.
%Y A379080 Cf. A200719, A379084.
%K A379080 nonn
%O A379080 0,2
%A A379080 _Seiichi Manyama_, Dec 15 2024