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

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• sign
• easy
• tabf

Comments

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).

Examples

			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).
		

Links

• W. Lang, First ten rows.

Crossrefs

Row sums A112693. Unsigned row sums A112694.