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Search: id:A104601
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| A104601 |
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Triangle T(r,n) read by rows: number of n X n (0,1)-matrices with exactly r entries equal to 1 and no zero row or columns. |
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+0
5
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| 1, 0, 2, 0, 4, 6, 0, 1, 45, 24, 0, 0, 90, 432, 120, 0, 0, 78, 2248, 4200, 720, 0, 0, 36, 5776, 43000, 43200, 5040, 0, 0, 9, 9066, 222925, 755100, 476280, 40320, 0, 0, 1, 9696, 727375, 6700500, 13003620, 5644800, 362880, 0, 0, 0, 7480, 1674840
(list; table; graph; listen)
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OFFSET
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1,3
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LINKS
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M. Maia and M. Mendez, On the arithmetic product of combinatorial species
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FORMULA
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T(r, n)=Sum{l>=r, Sum{d|l, (-1)^(2n-d-l/d)*C(n, d)*C(n, l/d)*C(l, r) }}.
E.g.f.: Sum(((1+x)^n-1)^n*exp((1-(1+x)^n)*y)*y^n/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 24 2008
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EXAMPLE
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1
0,2
0,4,6
0,1,45,24
0,0,90,432,120
0,0,78,2248,4200,720
0,0,36,5776,43000,43200,5040
0,0,9,9066,222925,755100,476280,40320
0,0,1,9696,727375,6700500,13003620,5644800,362880
0,0,0,7480,1674840,37638036,179494350,226262400,71850240,3628800
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CROSSREFS
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Right-edge diagonals include A000142, A055602, A055603. Row sums are in A104602.
Column sums are in A048291. The triangle read by columns = A055599.
Sequence in context: A068333 A121451 A096984 this_sequence A133144 A098123 A066659
Adjacent sequences: A104598 A104599 A104600 this_sequence A104602 A104603 A104604
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Mar 27 2005
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