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 A379082 #13 Dec 15 2024 06:43:45
%S A379082 1,2,5,16,64,288,1354,6496,31728,157818,798098,4091712,21211165,
%T A379082 110969430,585116287,3106334810,16590881379,89085610328,480627775528,
%U A379082 2604103448334,14163573236255,77302955664902,423245859576867,2324046398587426,12795255089638583,70617777139027756
%N A379082 Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^3)^2 ).
%F A379082 G.f. A(x) satisfies:
%F A379082 (1) A(x) = exp( Sum_{k>=1} A379085(k) * x^k/k ).
%F A379082 (2) A(x) = ( (1 + x*A(x)) * (1 + x^3*A(x)^(7/2)) )^2.
%F A379082 (3) A(x) = B(x)^2 where B(x) is the g.f. of A379089.
%F A379082 a(n) = (1/(n+1)) * [x^n] 1/( 1/(1 + x) - x^3 )^(2*(n+1)).
%F A379082 a(n) = 2 * Sum_{k=0..floor(n/3)} binomial(2*n+k+2,k) * binomial(2*n+k+2,n-3*k)/(2*n+k+2) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n+k+2,n-3*k).
%o A379082 (PARI) a(n) = 2*sum(k=0, n\3, binomial(2*n+k+2, k)*binomial(2*n+k+2, n-3*k)/(2*n+k+2));
%Y A379082 Cf. A198888, A379083.
%Y A379082 Cf. A379085, A379089.
%K A379082 nonn
%O A379082 0,2
%A A379082 _Seiichi Manyama_, Dec 15 2024