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 A144331 Triangle b(n,k) read by rows (n >= 0, 0 <= k <= 2n). See A144299 for definition and properties. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS 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. LINKS Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394, 2017. David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009) FORMULA 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)!). EXAMPLE 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   ... MATHEMATICA Flatten[ Table[ PadLeft[ Table[(n+k)!/(2^k*k!*(n-k)!), {k, 0, n}], 2*n+1, 0], {n, 0, 8}]] (* Jean-François Alcover, Oct 14 2011 *) PROG (Haskell) a144331 n k = a144331_tabf !! n !! k a144331_row n = a144331_tabf !! n a144331_tabf = iterate (\xs ->   zipWith (+) ([0] ++ xs ++ [0]) \$ zipWith (*) (0:[0..]) ([0, 0] ++ xs)) [1] -- Reinhard Zumkeller, Nov 24 2014 CROSSREFS 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: A110492 A225413 A180995 * A216805 A167259 A303650 Adjacent sequences:  A144328 A144329 A144330 * A144332 A144333 A144334 KEYWORD nonn,tabf,nice AUTHOR David Applegate and N. J. A. Sloane, Dec 07 2008 STATUS approved

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Last modified October 18 15:19 EDT 2019. Contains 328161 sequences. (Running on oeis4.)