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A144331
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Triangle b(n,k) read by rows (n >= 0, 0 <= k <= 2n). See A144299 for definition and properties.
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6
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1, 0, 1, 1, 0, 0, 1, 3, 3, 0, 0, 0, 1, 6, 15, 15, 0, 0, 0, 0, 1, 10, 45, 105, 105, 0, 0, 0, 0, 0, 1, 15, 105, 420, 945, 945, 0, 0, 0, 0, 0, 0, 1, 21, 210, 1260, 4725, 10395, 10395, 0, 0, 0, 0, 0, 0, 0, 1, 28, 378, 3150, 17325, 62370, 135135, 135135, 0, 0, 0, 0, 0, 0
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OFFSET
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0,8
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COMMENTS
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Although this entry is the last of the versions of the underlying triangle to be added to the OEIS, for some applications it is the most important.
Row n has 2n+1 entries.
A001498 has a b-file.
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LINKS
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Table of n, a(n) for n=0..69.
David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)
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FORMULA
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E.g.f.: Sum_{n >= 0} Sum_{k = 0..2n} b(n,k) y^n x^k/k! = exp(y(x+x^2/2)).
b(n,k) = n!/(2^(n-k)*(2*n-k)!*(k-n)!).
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EXAMPLE
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Triangle begins:
[1]
[0, 1, 1]
[0, 0, 1, 3, 3]
[0, 0, 0, 1, 6, 15, 15]
[0, 0, 0, 0, 1, 10, 45, 105, 105]
[0, 0, 0, 0, 0, 1, 15, 105, 420, 945, 945]
[0, 0, 0, 0, 0, 0, 1, 21, 210, 1260, 4725, 10395, 10395]
...
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MATHEMATICA
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Flatten[ Table[ PadLeft[ Table[(n+k)!/(2^k*k!*(n-k)!), {k, 0, n}], 2*n+1, 0], {n, 0, 8}]] (* From Jean-François Alcover, Oct 14 2011 *)
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CROSSREFS
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Cf. A144299. Row sums give A001515, column sums A000085.
Other versions of this triangle are given in A001497, A001498, A111924 and A100861.
See A144385 for a generalization.
Sequence in context: A199261 A110492 A180995 * A216805 A167259 A000876
Adjacent sequences: A144328 A144329 A144330 * A144332 A144333 A144334
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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David Applegate and N. J. A. Sloane, Dec 07 2008
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STATUS
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approved
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