cp's OEIS Frontend

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.

A368965 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ).

This page as a plain text file.
%I A368965 #17 Jan 13 2024 10:45:25
%S A368965 1,3,17,117,895,7309,62410,550431,4975297,45846977,429095387,
%T A368965 4067760593,38977419018,376901628882,3673226867356,36043590216621,
%U A368965 355800292078095,3530878133357175,35205183620396571,352505713454687599,3543078943592291301
%N A368965 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ).
%H A368965 Seiichi Manyama, <a href="/A368965/b368965.txt">Table of n, a(n) for n = 0..971</a>
%H A368965 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A368965 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(4*n-k+2,n-2*k).
%o A368965 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x-x^2)^2)/x)
%o A368965 (PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y A368965 Cf. A368961, A368967.
%Y A368965 Cf. A368966.
%K A368965 nonn
%O A368965 0,2
%A A368965 _Seiichi Manyama_, Jan 10 2024