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A079621
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Matrix square of unsigned Lah triangle abs(A008297(n,k)) or A105278(n,k).
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1
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1, 4, 1, 24, 12, 1, 192, 144, 24, 1, 1920, 1920, 480, 40, 1, 23040, 28800, 9600, 1200, 60, 1, 322560, 483840, 201600, 33600, 2520, 84, 1, 5160960, 9031680, 4515840, 940800, 94080, 4704, 112, 1, 92897280, 185794560, 108380160, 27095040, 3386880, 225792
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OFFSET
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1,2
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COMMENTS
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Also the number of k-dimensional flats of the extended Shi arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -1 <= d <= 2). - Shuhei Tsujie, Apr 26 2019
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LINKS
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FORMULA
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E.g.f.: exp(x*y/(1-2*x)).
The n-th row polynomial equals x o (x + 2) o (x + 4) o ... o (x + 2*n), where o is the deformed Hadamard product of power series defined in Bala, section 3.1. - Peter Bala, Jan 18 2018
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EXAMPLE
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Triangle begins:
1;
4, 1;
24, 12, 1;
192, 144, 24, 1;
1920, 1920, 480, 40, 1;
...
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MAPLE
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# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
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MATHEMATICA
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BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[2^#*(#+1)!&, rows = 12];
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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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