login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124503 Triangle read by rows: T(n,k) is the number of set partitions of the set {1,2,...,n} (or of any n-set) containing k blocks of size 3 (0<=k<=floor(n/3)). 4
1, 1, 2, 4, 1, 11, 4, 32, 20, 113, 80, 10, 422, 385, 70, 1788, 1792, 560, 8015, 9492, 3360, 280, 39435, 50640, 23100, 2800, 204910, 295020, 147840, 30800, 1144377, 1763300, 1044120, 246400, 15400, 6722107, 11278410, 7241520, 2202200, 200200, 41877722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row n contains 1+floor(n/3) terms. Row sums yield the Bell numbers (A000110). T(n,0)=A124504(n). Sum(k*T(n,k), k=0..floor(n/3))=A105480(n+1).

LINKS

Alois P. Heinz, Rows n = 0..250, flattened

FORMULA

E.g.f.: G(t,z) = exp(exp(z)-1+(t-1)z^3/6).

EXAMPLE

T(4,1)=4 because we have 1|234, 134|2, 124|3 and 123|4.

Triangle starts:

1;

1;

2;

4, 1;

11, 4;

32, 20;

113, 80, 10;

422, 385, 70;

...

MAPLE

G:=exp(exp(z)-1+(t-1)*z^3/6): Gser:=simplify(series(G, z=0, 17)): for n from 0 to 14 do P[n]:=sort(n!*coeff(Gser, z, n)) od: for n from 0 to 14 do seq(coeff(P[n], t, k), k=0..floor(n/3)) od; # yields sequence in triangular form

# second Maple program:

with(combinat):

b:= proc(n, i) option remember; expand(`if`(n=0, 1,

`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*

b(n-i*j, i-1)*`if`(i=3, x^j, 1), j=0..n/i))))

end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)):

seq(T(n), n=0..15); # Alois P. Heinz, Mar 08 2015

MATHEMATICA

nn = 8; k = 3; Range[0, nn]! CoefficientList[

Series[Exp[Exp[x] - 1 + (y - 1) x^k/k!], {x, 0, nn}], {x, y}] // Grid

// Geoffrey Critzer, Aug 26 2012

CROSSREFS

Cf. A000110, A124504, A105480, A355144.

T(3n,n) gives A025035.

Sequence in context: A308300 A246188 A135333 * A114499 A030730 A117131

Adjacent sequences: A124500 A124501 A124502 * A124504 A124505 A124506

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Nov 14 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 07:00 EST 2022. Contains 358649 sequences. (Running on oeis4.)