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A019576 Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives triangle of numbers f(n,k)/n. 7
1, 1, 1, 2, 6, 1, 6, 45, 12, 1, 24, 420, 160, 20, 1, 120, 4800, 2450, 375, 30, 1, 720, 65520, 43050, 7560, 756, 42, 1, 5040, 1045170, 858480, 167825, 19208, 1372, 56, 1, 40320, 19126800, 19208000, 4110120, 516096, 43008, 2304, 72, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

T(n,k) is 1/n times the number of endofunctions on [n] such that the maximal cardinality of the nonempty preimages equals k. - Alois P. Heinz, May 23 2016

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

FORMULA

T(n,k) = A019575(n,k)/n.

EXAMPLE

:   1;

:   1,     1;

:   2,     6,     1;

:   6,    45,    12,    1;

:  24,   420,   160,   20,   1;

: 120,  4800,  2450,  375,  30,  1;

: 720, 65520, 43050, 7560, 756, 42, 1;

MAPLE

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

      add(b(n-j, i-1, k)/j!, j=0..min(k, n))))

    end:

T:= (n, k)-> (n-1)!* (b(n$2, k) -b(n$2, k-1)):

seq(seq(T(n, k), k=1..n), n=1..12);  # Alois P. Heinz, Jul 29 2014

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i<1, 0, Sum[b[n-j, i-1, k]/j!, {j, 0, Min[k, n]}]]]; T[n_, k_] := (n-1)!*(b[n, n, k]-b[n, n, k-1]); Table[Table[T[n, k], {k, 1, n}], {n, 1, 12}] // Flatten (* Jean-Fran├žois Alcover, Jan 15 2015, after Alois P. Heinz *)

CROSSREFS

Row sums give A000169.

Cf. A019575.

Sequence in context: A288872 A191100 A322944 * A141906 A136766 A199501

Adjacent sequences:  A019573 A019574 A019575 * A019577 A019578 A019579

KEYWORD

nonn,tabl,easy,nice

AUTHOR

Lee Corbin (lcorbin(AT)tsoft.com)

STATUS

approved

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Last modified June 25 12:01 EDT 2019. Contains 324352 sequences. (Running on oeis4.)