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 A151511 The triangle in A151359 read by rows downwards. 5
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS 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 LINKS Table of n, a(n) for n=0..69. 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 [math.CO], 2009 (see Table 7 E5(n,k) page 16). FORMULA 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 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 1 31 90 65 15 1 0 0 63 301 350 140 21 1 0 0 119 966 1701 1050 266 28 1 MATHEMATICA 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 *) PROG (Sage) # uses[bell_matrix from A264428] bell_matrix(lambda n: 1 if n<6 else 0, 12) # Peter Luschny, Jan 19 2016 CROSSREFS Begins in same way as triangle of Stirling numbers of second kind, A048993, but is strictly different. N. J. A. Sloane, Aug 09 2017 Cf. A148092 (row sums), A122848, A111246, A144644, A151509. Sequence in context: A144644 A151509 A264434 * A048993 A264431 A357941 Adjacent sequences: A151508 A151509 A151510 * A151512 A151513 A151514 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 06:37 EDT 2024. Contains 375085 sequences. (Running on oeis4.)