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A059374
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Triangle read by rows, T(n, k) = Sum_{i=0..n} L'(n, n-i) * binomial(i, k), for k = 0..n-1.
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1
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1, 3, 2, 13, 18, 6, 73, 156, 108, 24, 501, 1460, 1560, 720, 120, 4051, 15030, 21900, 15600, 5400, 720, 37633, 170142, 315630, 306600, 163800, 45360, 5040, 394353, 2107448, 4763976, 5891760, 4292400, 1834560, 423360, 40320
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OFFSET
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1,2
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COMMENTS
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L'(n, i) are unsigned Lah numbers (Cf. A008297).
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
[1],
[3, 2],
[13, 18, 6],
[73, 156, 108, 24],
[501, 1460, 1560, 720, 120],
...
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MATHEMATICA
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t[n_, k_] := Sum[ Binomial[n-1, n-i-1]*n!/(n-i)!*Binomial[i, k], {i, 0, n}]; Table[t[n, k], {n, 1, 8}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Mar 22 2013 *)
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PROG
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(PARI) for(n=1, 10, for(k=0, n-1, print1(sum(j=0, n, binomial(j, k)* binomial(n-1, n-j-1)*n!/(n-j)!), ", "))) \\ G. C. Greubel, Jan 29 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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