A112693 -id:A112693 - cp's OEIS frontend

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

1, 3, -1, -6, 6, -9, -70, 163, -42, -72, 30, -123, -1110, 8440, -18244, 2423, 43036, -53172, 11232, 8640, 90, -792, -7425, 137760, -771911, 1624514, 2262109, -21114844, 51074797, -54783526, 6214788, 45596664, -40513824, 7309440, 3110400, 630, -10278, -86841, 3685605, -41159454

Offset: 0

Wolfdieter Lang, Oct 14 2005

The sequence of row lengths is A000217 (triangular numbers): [1, 3, 6, 10, 15, 21,..].

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).

			Rows: [1]; [3,-1,-6]; [6,-9,-70,163,-42,-72];...
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).

W. Lang, First ten rows.

Row sums A112693. Unsigned row sums A112694.

A112694 Row sums of unsigned array A112692.

Original entry on oeis.org

1, 10, 362, 146450, 234522884, 6807857991672, 869962821793011472, 2352463379908322901560928, 36305094521738344415450726082096, 13237525270352155405709985211985066209696

Offset: 0

Wolfdieter Lang, Oct 14 2005

Signed row sums A112693.

a(n)=sum(|A112692(k, m)|, m=0..((k+1)*(k+2)/2)-1), k>=0.

cp's OEIS Frontend

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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A112694 Row sums of unsigned array A112692.

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