A158471 - OEIS

A158471

Stirling-like triangle by rows generated from (x-1)*(x-1)*(x-2)*(x-3)*(x-4)*...

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

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OFFSET

0,5

COMMENTS

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

LINKS

Table of n, a(n) for n=0..51.

FORMULA

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 n X n matrix with (1,1,2,3,4,...) in the diagonal and the rest zeros.

EXAMPLE

First few rows of the unsigned triangle =

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;