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!)
A262078 Number T(n,k) of partitions of an n-set with distinct block sizes and maximal block size equal to k; triangle T(n,k), k>=0, k<=n<=k*(k+1)/2, read by columns. 4
1, 1, 1, 3, 1, 4, 10, 60, 1, 5, 15, 140, 280, 1260, 12600, 1, 6, 21, 224, 630, 3780, 34650, 110880, 360360, 2522520, 37837800, 1, 7, 28, 336, 1050, 7392, 74844, 276276, 1513512, 9459450, 131171040, 428828400, 2058376320, 9777287520, 97772875200, 2053230379200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Columns k = 0..36, flattened

EXAMPLE

Triangle T(n,k) begins:

: 1;

:    1;

:       1;

:       3,  1;

:           4,     1;

:          10,     5,    1;

:          60,    15,    6,    1;

:                140,   21,    7,   1;

:                280,  224,   28,   8,  1;

:               1260,  630,  336,  36,  9,  1;

:              12600, 3780, 1050, 480, 45, 10, 1;

MAPLE

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,

       b(n, i-1) +`if`(i>n, 0, binomial(n, i)*b(n-i, i-1))))

    end:

T:= (n, k)-> b(n, k) -`if`(k=0, 0, b(n, k-1)):

seq(seq(T(n, k), n=k..k*(k+1)/2), k=0..7);

MATHEMATICA

b[n_, i_] := b[n, i] = If[i*(i+1)/2<n, 0, If[n==0, 1, b[n, i-1] + If[i>n, 0, Binomial[n, i]*b[n-i, i-1]]]]; T[n_, k_] :=  b[n, k] - If[k==0, 0, b[n, k-1]]; Table[T[n, k], {k, 0, 7}, {n, k, k*(k+1)/2}] // Flatten (* Jean-Fran├žois Alcover, Dec 18 2016, after Alois P. Heinz *)

CROSSREFS

Row sums give A007837.

Column sums give A262073.

Cf. A000217, A002024, A262071, A262072 (same read by rows).

Sequence in context: A137405 A322456 A301701 * A121922 A054631 A180063

Adjacent sequences:  A262075 A262076 A262077 * A262079 A262080 A262081

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Sep 10 2015

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 September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)