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 A151509 The triangle in A151338 read by rows downwards. 4
 1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 7, 6, 1, 0, 1, 15, 25, 10, 1, 0, 0, 31, 90, 65, 15, 1, 0, 0, 56, 301, 350, 140, 21, 1, 0, 0, 91, 938, 1701, 1050, 266, 28, 1, 0, 0, 126, 2737, 7686, 6951, 2646, 462, 36, 1, 0, 0, 126, 7455, 32725, 42315, 22827, 5880, 750, 45, 1, 0, 0, 0, 18711, 132055 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS The Bell transform of the sequence "g(n) = 1 if n < 5, otherwise 0". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016 LINKS Table of n, a(n) for n=0..70. Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017. David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009 (see Table 6 E4(n,k) page 15). FORMULA Bivariate e.g.f A151509(x,t) = Sum_{n>=0, k>=0} T(n,k)*x^n*t^k/n! = exp(t*G5(x)), where G5(x) = Sum_{i=1..5} x^i/i! is the e.g.f. of column 1. - R. J. Mathar, May 28 2019 EXAMPLE Triangle begins: 1; 0, 1; 0, 1, 1; 0, 1, 3, 1; 0, 1, 7, 6, 1; 0, 1, 15, 25, 10, 1; 0, 0, 31, 90, 65, 15, 1; 0, 0, 56, 301, 350, 140, 21, 1; 0, 0, 91, 938, 1701, 1050, 266, 28, 1; MATHEMATICA rows = 10; BellMatrix[f_Function | f_Symbol, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]]; B = BellMatrix[If[# < 5, 1, 0]&, rows]; Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *) PROG (Sage) # uses[bell_matrix from A264428] bell_matrix(lambda n: 1 if n<5 else 0, 12) # Peter Luschny, Jan 19 2016 CROSSREFS Cf. A110038 (row sums), A122848, A111246, A144644, A151511. Sequence in context: A272008 A054024 A144644 * A264434 A151511 A048993 Adjacent sequences: A151506 A151507 A151508 * A151510 A151511 A151512 KEYWORD nonn,tabl,easy AUTHOR N. J. A. Sloane, May 14 2009 EXTENSIONS Row 9 added by Michel Marcus, Feb 13 2014 More rows from R. J. Mathar, May 28 2019 STATUS approved

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Last modified August 12 04:50 EDT 2024. Contains 375085 sequences. (Running on oeis4.)