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A126353
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Triangle read by rows: matrix product of the Stirling numbers of the first kind with the binomial coefficients.
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4
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1, 1, 0, 1, -1, 1, 1, -3, 5, -2, 1, -6, 17, -20, 9, 1, -10, 45, -100, 109, -44, 1, -15, 100, -355, 694, -689, 265, 1, -21, 196, -1015, 3094, -5453, 5053, -1854, 1, -28, 350, -2492, 10899, -29596, 48082, -42048, 14833
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| Many well-known integer sequences arise from such a matrix product of combinatorial coefficients. In the present case we have as the first row A000166 = subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
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FORMULA
| (In Maple notation:) Matrix product B.A of matrix A[i,j]:=binomial(j-1,i-1) with i = 1 to p+1, j = 1 to p+1, p=8 and of matrix B[i,j]:=stirling1(j,i) with i from 1 to d, j from 1 to d, d=9.
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EXAMPLE
| Matrix begins:
1 0 1 -2 9 -44 265 -1854 14833
0 1 -1 5 -20 109 -689 5053 -42048
0 0 1 -3 17 -100 694 -5453 48082
0 0 0 1 -6 45 -355 3094 -29596
0 0 0 0 1 -10 100 -1015 10899
0 0 0 0 0 1 -15 196 -2492
0 0 0 0 0 0 1 -21 350
0 0 0 0 0 0 0 1 -28
0 0 0 0 0 0 0 0 1
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CROSSREFS
| Signed version of A094791 [from Olivier Gerard, Jul 31 2011]
Cf. A039810, A039814, A126350, A126351, A054654.
Sequence in context: A197521 A161865 A145325 * A094791 A115406 A059246
Adjacent sequences: A126350 A126351 A126352 * A126354 A126355 A126356
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KEYWORD
| tabl,sign
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AUTHOR
| Thomas Wieder (thomas.wieder(AT)t-online.de), Dec 29 2006
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