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.

A112692 Coefficient array of numerator polynomials of o.g.f.s (rising powers) for the columns of triangle A008517 (second-order Eulerian numbers).

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%I A112692 #7 Aug 29 2019 17:32:10
%S A112692 1,3,-1,-6,6,-9,-70,163,-42,-72,30,-123,-1110,8440,-18244,2423,43036,
%T A112692 -53172,11232,8640,90,-792,-7425,137760,-771911,1624514,2262109,
%U A112692 -21114844,51074797,-54783526,6214788,45596664,-40513824,7309440,3110400,630,-10278,-86841,3685605,-41159454
%N A112692 Coefficient array of numerator polynomials of o.g.f.s (rising powers) for the columns of triangle A008517 (second-order Eulerian numbers).
%C A112692 The sequence of row lengths is A000217 (triangular numbers): [1, 3, 6, 10, 15, 21,..].
%C A112692 The o.g.f. of the k-th column sequence of triangle A008517(n,k), n>=k>=1, is (2^floor(k/2))*(x^k)*p(k,x)/product((1-j*x)^(k+1-j),j=1..k), k>=2, with the row polynomials p(k,x):= sum(a(k-2,m)*x^m,m=0..(k*(k-1)/2)-1).
%H A112692 W. Lang, <a href="/A112692/a112692.txt">First ten rows.</a>
%e A112692 Rows: [1]; [3,-1,-6]; [6,-9,-70,163,-42,-72];...
%e A112692 The k=3, offset 3, column sequence [6,58,328,..] of A008517 has o.g.f. 2*(x^3)*(3-x-6*x^2)/product((1-j*x)^(4-j),j=1..3).
%Y A112692 Row sums A112693. Unsigned row sums A112694.
%K A112692 sign,easy,tabf
%O A112692 0,2
%A A112692 _Wolfdieter Lang_, Oct 14 2005