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 A151512 The triangle in A151359 read by rows upwards. 1
 1, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 7, 1, 0, 1, 10, 25, 15, 1, 0, 1, 15, 65, 90, 31, 1, 0, 1, 21, 140, 350, 301, 63, 0, 0, 1, 28, 266, 1050, 1701, 966, 119, 0, 0, 1, 36, 462, 2646, 6951, 7770, 2989, 210, 0, 0, 1, 45, 750, 5880, 22827, 42525, 33985, 8925, 336, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Conjectured: The i-th element of row j is the number of different equivalence relationships, within a set of (j-1) element, having (j-i) equivalence classes. For example: row 5 = [1, 6, 7, 1, 0] means that, in a set of 4 elements, there exists 7 equivalence relationships having 3 different equivalence classes. - Philippe Beaudoin, Nov 09 2013 LINKS 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) (see Table 7 E5(n,k) page 16). EXAMPLE Triangle begins:   1   1  0   1  1   0   1  3   1    0   1  6   7    1    0   1 10  25   15    1   0   1 15  65   90   31   1   0   1 21 140  350  301  63   0 0   1 28 266 1050 1701 966 119 0 0 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[Table[t[n - 1, k], {k, n - 1, 0, -1}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Jan 20 2016, using Peter Luschny's Bell transform *) CROSSREFS Cf. A148092 (row sums), A151511 (row-reversed). Sequence in context: A085791 A144645 A151510 * A106800 A308484 A227320 Adjacent sequences:  A151509 A151510 A151511 * A151513 A151514 A151515 KEYWORD nonn,tabl,easy AUTHOR N. J. A. Sloane, May 14 2009 EXTENSIONS Row 9 added by Michel Marcus, Feb 13 2014 Row 10  from R. J. Mathar, May 28 2019 STATUS approved

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Last modified April 18 03:09 EDT 2021. Contains 343072 sequences. (Running on oeis4.)