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A089258
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Another version of A080955.
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2
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1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 3, 5, 6, 9, 1, 4, 10, 16, 24, 44, 1, 5, 17, 38, 65, 120, 265, 1, 6, 26, 78, 168, 326, 720, 1854, 1, 7, 37, 142, 393, 872, 1957, 5040, 14833, 1, 8, 50, 236, 824, 2208, 5296, 13700, 40320, 133496
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| For n>0, T(n, k) is the permanent of the n X n matrix with k on the diagonal and 1 elsewhere; T(0, k) = 1. T(n, k) = Sum(j>=0; A008290(n, j)*k^j). T(n, k) = n*T(n-1, k) + (k-1)^n . T(n, k) = n!*Sum(j=0..n; (k-1)^j/j! ) For column k, E.g.f. : exp((k-1)*x/(1-x)).
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EXAMPLE
| Row n=0: 1, 1, 1, 1, 1, 1, 1, 1, ...
Row n=1: 0, 1, 2, 3, 4, 5, 6, 7, ...
Row n=2: 1, 2, 5, 10, 17, 26, 37, ...
Row n=3: 2, 6, 16, 38, 78, 152, 236, ...
Row n=4: 9, 24, 65, 168, 393, 824, ...
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CROSSREFS
| Columns give : A000166 A000142 A000522 A010852 A053486 A053487 A080954
Cf. A080955 A008290.
Sequence in context: A055253 A103626 A026268 * A004065 A127496 A144393
Adjacent sequences: A089255 A089256 A089257 * A089259 A089260 A089261
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 12 2003
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