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.

A368973 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^2)^2 ).

This page as a plain text file.
%I A368973 #15 Jan 13 2024 10:45:57
%S A368973 1,3,13,65,351,1989,11650,69903,427225,2649229,16622079,105310673,
%T A368973 672687322,4327037010,28002409452,182179075689,1190778886791,
%U A368973 7815755146095,51491064226095,340374137775879,2256891800364421,15006481967365535,100037043223408890
%N A368973 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^2)^2 ).
%H A368973 Seiichi Manyama, <a href="/A368973/b368973.txt">Table of n, a(n) for n = 0..1000</a>
%H A368973 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A368973 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n+k+1,k) * binomial(4*n-k+2,n-2*k).
%o A368973 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x+x^2)^2)/x)
%o A368973 (PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y A368973 Cf. A368969, A368975.
%Y A368973 Cf. A368965.
%K A368973 nonn
%O A368973 0,2
%A A368973 _Seiichi Manyama_, Jan 10 2024