login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..65.

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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