0,5

Row sums of the unsigned triangle = A098558: (1, 2, 4, 12, 48, 240, 1440, 10080,...).

Triangle read by rows, n-th row = n-th degree polynomial with alternating signs generated from n terms of a*b*c*d...; where a,b,c...= (x-1), (x-1), (x-2), (x-3), (x-4),... n-th row, n>0 = charpoly of an nxn matrix with (1,1,2,3,4,...) in the diagonal and the rest zeros.

First few rows of the unsigned triangle =

1;

1, 1;

1, 2, 1;

1, 4, 5, 2;

1, 7, 17, 17, 6;

1, 11, 45, 85, 74, 24;

1, 16, 100, 310, 499, 394, 120;

1, 22, 196, 910, 2359, 3388, 2484, 720;

1, 29, 350, 2282, 8729, 19901, 26200, 18108, 5040;

1, 37, 582, 5082, 26985, 89733, 185408, 227708, 149904, 40320;

1, 46, 915, 10320, 72723, 332598, 993005, 1896380, 2199276, 1389456, 362880;

...

Example: Row 5 = x^5 - 11x^4 + 45x^3 -85x^2 + 74x - 24 =

(x-1)*(x-1)*(x-2)*(x-3)*(x-4)

A098558

Cf. A103718. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 20 2009]

Sequence in context: A129704 A144460 A057785 this_sequence A158472 A118686 A102610

Adjacent sequences: A158468 A158469 A158470 this_sequence A158472 A158473 A158474

tabl,sign

Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009