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 A379083 #13 Dec 15 2024 06:44:50
%S A379083 1,3,12,58,321,1941,12405,82188,558567,3870694,27245268,194269872,
%T A379083 1400352702,10187886330,74710928103,551676261727,4098401671788,
%U A379083 30610414484517,229717037309281,1731295701244008,13098454442320593,99444838611953627,757393732018935552,5785220154325055826
%N A379083 Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^3)^3 ).
%F A379083 G.f. A(x) satisfies:
%F A379083 (1) A(x) = exp( Sum_{k>=1} A379087(k) * x^k/k ).
%F A379083 (2) A(x) = ( (1 + x*A(x)) * (1 + x^3*A(x)^(10/3)) )^3.
%F A379083 (3) A(x) = B(x)^3 where B(x) is the g.f. of A379090.
%F A379083 a(n) = (1/(n+1)) * [x^n] 1/( 1/(1 + x) - x^3 )^(3*(n+1)).
%F A379083 a(n) = 3 * Sum_{k=0..floor(n/3)} binomial(3*n+k+3,k) * binomial(3*n+k+3,n-3*k)/(3*n+k+3) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(3*n+k+3,n-3*k).
%o A379083 (PARI) a(n) = 3*sum(k=0, n\3, binomial(3*n+k+3, k)*binomial(3*n+k+3, n-3*k)/(3*n+k+3));
%Y A379083 Cf. A198888, A379082.
%Y A379083 Cf. A379087, A379090.
%K A379083 nonn
%O A379083 0,2
%A A379083 _Seiichi Manyama_, Dec 15 2024