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A144644 Triangle in A144643 read by columns downwards. 4
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 7, 6, 1, 0, 0, 15, 25, 10, 1, 0, 0, 25, 90, 65, 15, 1, 0, 0, 35, 280, 350, 140, 21, 1, 0, 0, 35, 770, 1645, 1050, 266, 28, 1, 0, 0, 0, 1855, 6930, 6825, 2646, 462, 36, 1, 0, 0, 0, 3675, 26425, 39795, 22575, 5880, 750, 45, 1, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

The Bell transform of the sequence "g(n) = 1 if n<4 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..67.

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.

FORMULA

Bivariate e.g.f. A144644(x,t) = Sum_{n>=0, k>=0} T(n,k)*x^n*t^k/n! = exp(t*G4(x)), where G4(x) = Sum_{i=1..4} 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

0,0,15,25,10,1

0,0,25,90,65,15,1

0,0,35,280,350,140,21,1

0,0,35,770,1645,1050,266,28,1

0,0,0,1855,6930,6825,2646,462,36,1

0,0,0,3675,26425,39795,22575,5880,750,45,1

0,0,0,5775,90475,211750,172095,63525,11880,1155,55,1

0,0,0,5775,275275,1033725,1198120,609840,158235,22275,1705,66,1

0,0,0,0,725725,4629625,7702695,5335330,1861860,358215,39325,2431,78,1

0,0,0,0,1576575,18918900,45965920,43158115,19899880,5060055,750750,66066,3367,91,1

0,0,0,0,2627625,69719650,254879625,325475150,196471275,64689625,12522510,1476475,106470,4550,105,1

MATHEMATICA

With[{r = 15}, Table[BellY[n, k, {1, 1, 1, 1}], {n, 0, r}, {k, 0, n}]] (* Jan Mangaldan, May 22 2016 *)

PROG

(Sage) # uses[bell_matrix from A264428]

bell_matrix(lambda n: 1 if n<4 else 0, 12) # Peter Luschny, Jan 19 2016

(Pari) \\ Function bell_matrix is defined in A264428.

B = bell_matrix( n -> {if(n < 4, 1, 0)}, 9); for(n = 0, 9, printp(); for(k = 1, n, print1(B[n, k], " "))); \\ Peter Luschny, Apr 17 2019

CROSSREFS

Cf. A001681 (row sums), A122848, A111246, A151509, A151511.

Sequence in context: A213060 A272008 A054024 * A151509 A264434 A151511

Adjacent sequences:  A144641 A144642 A144643 * A144645 A144646 A144647

KEYWORD

nonn,tabl

AUTHOR

David Applegate and N. J. A. Sloane, Jan 25 2009

STATUS

approved

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Last modified May 25 10:50 EDT 2020. Contains 334592 sequences. (Running on oeis4.)