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!)
A276922 Number T(n,k) of ordered set partitions of [n] where the maximal block size equals k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 13
1, 0, 1, 0, 2, 1, 0, 6, 6, 1, 0, 24, 42, 8, 1, 0, 120, 330, 80, 10, 1, 0, 720, 2970, 860, 120, 12, 1, 0, 5040, 30240, 10290, 1540, 168, 14, 1, 0, 40320, 345240, 136080, 21490, 2464, 224, 16, 1, 0, 362880, 4377240, 1977360, 326970, 38808, 3696, 288, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

E.g.f. for column k>0: 1/(1-Sum_{i=1..k} x^i/i!) - 1/(1-Sum_{i=1..k-1} x^i/i!).

T(n,k) = A276921(n,k) - A276921(n,k-1) for k>0. T(n,0) = A000007(0).

EXAMPLE

Triangle T(n,k) begins:

  1;

  0,     1;

  0,     2,      1;

  0,     6,      6,      1;

  0,    24,     42,      8,     1;

  0,   120,    330,     80,    10,    1;

  0,   720,   2970,    860,   120,   12,   1;

  0,  5040,  30240,  10290,  1540,  168,  14,  1;

  0, 40320, 345240, 136080, 21490, 2464, 224, 16, 1;

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 1, add(

       A(n-i, k)*binomial(n, i), i=1..min(n, k)))

    end:

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

seq(seq(T(n, k), k=0..n), n=0..10);

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - i, k]*Binomial[n, i], {i, 1, Min[n, k]}]]; T[n_, k_] :=  A[n, k] - If[k == 0, 0, A[n, k - 1]]; Table[T[n, k], {n, 0, 10}, { k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 11 2017, translated from Maple *)

CROSSREFS

Columns k=0-10 give: A000007, A000142 (for n>0), A320758, A320759, A320760, A320761, A320762, A320763, A320764, A320765, A320766.

Row sums give A000670.

T(2n,n) gives A276923.

Cf. A080510, A276921.

Sequence in context: A111184 A111596 A271703 * A129062 A281662 A163936

Adjacent sequences:  A276919 A276920 A276921 * A276923 A276924 A276925

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 22 2016

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 February 19 19:21 EST 2020. Contains 332047 sequences. (Running on oeis4.)