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A144633
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Triangle of 3-restricted Stirling numbers of the first kind (T(n,k), 0 <= k <= n), read by rows.
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6
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1, 0, 1, 0, -1, 1, 0, 2, -3, 1, 0, -5, 11, -6, 1, 0, 10, -45, 35, -10, 1, 0, 35, 175, -210, 85, -15, 1, 0, -910, -315, 1225, -700, 175, -21, 1, 0, 11935, -6265, -5670, 5565, -1890, 322, -28, 1, 0, -134750, 139755, -5005, -39270, 19425, -4410, 546, -36, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Definition: take the triangle in A144385, write it as an (infinite) upper triangular square matrix, invert it and transpose it.
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REFERENCES
| J. Y. Choi and J. D. H. Smith, The Tri-restricted Numbers and Powers of Permutation Representations, J. Comb. Math. Comb. Comp. 42 (2002), 113-125.
J. Y. Choi and J. D. H. Smith, On the Unimodality and Combinatorics of the Bessel Numbers, Discrete Math., 264 (2003), 45-53.
J. Y. Choi and J. D. H. Smith, On the combinatorics of multi-restricted numbers, Ars. Com., 75(2005), pp. 44-63.
J. Y. Choi et al., Reciprocity for multirestricted Stirling numbers, J. Combin. Theory 113 A (2006), 1050-1060.
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LINKS
| Alois P. Heinz, Rows n = 0..140, flattened
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, -1, 1;
0, 2, -3, 1;
0, -5, 11, -6, 1;
0, 10, -45, 35, -10, 1;
0, 35, 175, -210, 85, -15, 1;
0, -910, -315, 1225, -700, 175, -21, 1;
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MAPLE
| A:= proc(n, k) option remember; if n=k then 1 elif k<n or n<1 then 0 else A(n-1, k-1) +(k-1) *A(n-1, k-2) +(k-1) *(k-2) *A(n-1, k-3)/2 fi end: M:= proc(n) option remember; Matrix(n+1, (i, j)-> A(i-1, j-1))^(-1) end: T:= (n, k)-> M (n+1)[k+1, n+1]: seq (seq (T(n, k), k=0..n), n=0..12); # Alois P. Heinz, Oct 23 2009
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CROSSREFS
| For another version of this triangle see A144634.
Columns give A144636-A144639.
Sequence in context: A081247 A173050 A172380 * A005210 A048994 A132393
Adjacent sequences: A144630 A144631 A144632 * A144634 A144635 A144636
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KEYWORD
| sign,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 21 2009
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EXTENSIONS
| Corrected and extended by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009
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