A260612 - OEIS

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A260612

Triangle read by rows: T(n,k) = coefficient of x^(n-k) in Product_{m=0..n-1} (x+(-1)^m*m!), 0 <= k <= n.

1, 1, 1, 1, 0, -1, 1, 2, -1, -2, 1, -4, -13, 4, 12, 1, 20, -109, -308, 108, 288, 1, -100, -2509, 12772, 37068, -12672, -34560, 1, 620, -74509, -1793708, 9232908, 26676288, -9158400, -24883200, 1, -4420, -3199309, 373731652, 9049521228, -46507180032, -134457649920, 46133452800, 125411328000

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 0..1034 (first 120 terms from Matthew Campbell)

FORMULA

T(n, 1) = A058006(n-1) = (-1)^(n+1)*A153229(n) for n >= 1.

EXAMPLE

Row 0: 1.

Row 1: (x+(-1)^(0)*0!) = x+1. Coefficients are 1 and 1.

Row 2: (x+(-1)^0*0!)*(x+(-1)^(1)*1!) = (x+1)*(x-1) = x^2-1. Coefficients are 1, 0, and -1.

Row 3: (x+(-1)^(0)*0!)*(x-(-1)^(1)*1!)*(x+(-1)^(2)*2!) = (x+1)*(x-1)*(x+2) = x^3 + 2*x^2 - x - 2. Coefficients are 1, 2, -1, and -2.