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