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A151511
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The triangle in A151359 read by rows downwards.
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5
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1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 7, 6, 1, 0, 1, 15, 25, 10, 1, 0, 1, 31, 90, 65, 15, 1, 0, 0, 63, 301, 350, 140, 21, 1, 0, 0, 119, 966, 1701, 1050, 266, 28, 1, 0, 0, 210, 2989, 7770, 6951, 2646, 462, 36, 1, 0, 0, 336, 8925, 33985, 42525, 22827, 5880, 750, 45, 1, 0, 0, 462, 25641
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refs;
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OFFSET
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0,9
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COMMENTS
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The Bell transform of g(n) = 1 if n<6 else 0. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016
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LINKS
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David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009 (see Table 7 E5(n,k) page 16).
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FORMULA
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Bivariate e.g.f. A151511(x,t) = Sum_{n>=0, k>=0} T(n,k)*x^n*t^k/n! = exp(t*G6(x)), where G6(x) = Sum_{i=1..6} x^i/i! is the e.g.f. of column 1. - R. J. Mathar, May 28 2019
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EXAMPLE
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Triangle begins:
1
0 1
0 1 1
0 1 3 1
0 1 7 6 1
0 1 15 25 10 1
0 1 31 90 65 15 1
0 0 63 301 350 140 21 1
0 0 119 966 1701 1050 266 28 1
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MATHEMATICA
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Unprotect[Power]; 0^0 = 1; a[n_ /; 1 <= n <= 6] = 1; a[_] = 0; T[n_, k_] := T[n, k] = If[k == 0, a[0]^n, Sum[Binomial[n - 1, j - 1] a[j] T[n - j, k - 1], {j, 0, n - k + 1}]]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 20 2016, after Peter Luschny *)
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PROG
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(Sage) # uses[bell_matrix from A264428]
bell_matrix(lambda n: 1 if n<6 else 0, 12) # Peter Luschny, Jan 19 2016
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CROSSREFS
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Begins in same way as triangle of Stirling numbers of second kind, A048993, but is strictly different. N. J. A. Sloane, Aug 09 2017
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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