

A126353


Triangle read by rows: matrix product of the Stirling numbers of the first kind with the binomial coefficients.


4



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
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OFFSET

1,8


COMMENTS

Many wellknown 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.


LINKS

Table of n, a(n) for n=1..45.


FORMULA

(In Maple notation:) Matrix product B.A of matrix A[i,j]:=binomial(j1,i1) 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.


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


CROSSREFS

Signed version of A094791 [from Olivier Gérard, Jul 31 2011]
Cf. A039810, A039814, A126350, A126351, A054654.
Sequence in context: A282194 A308180 A329633 * A094791 A243524 A272300
Adjacent sequences: A126350 A126351 A126352 * A126354 A126355 A126356


KEYWORD

tabl,sign


AUTHOR

Thomas Wieder, Dec 29 2006


STATUS

approved



