The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A320759

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A320759

Number of ordered set partitions of [n] where the maximal block size equals three.
(history; published version)

#7 by N. J. A. Sloane at Mon Dec 14 05:13:21 EST 2020

STATUS

proposed

approved

#6 by Jean-François Alcover at Mon Dec 14 03:18:16 EST 2020

STATUS

editing

proposed

#5 by Jean-François Alcover at Mon Dec 14 03:18:12 EST 2020

MATHEMATICA

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];

a[n_] := With[{k = 3}, b[n, k] - b[n, k-1]];

a /@ Range[3, 25] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

STATUS

approved

editing

#4 by Alois P. Heinz at Sat Oct 20 17:39:07 EDT 2018

STATUS

editing

approved

#3 by Alois P. Heinz at Sat Oct 20 17:39:04 EDT 2018

LINKS

Alois P. Heinz, <a href="/A320759/b320759.txt">Table of n, a(n) for n = 3..424</a>

#2 by Alois P. Heinz at Sat Oct 20 17:37:31 EDT 2018

NAME

allocated for Alois P. Heinz

Number of ordered set partitions of [n] where the maximal block size equals three.

DATA

1, 8, 80, 860, 10290, 136080, 1977360, 31365600, 539847000, 10026139200, 199937337600, 4262167509600, 96744738090000, 2329950823200000, 59348032327584000, 1594257675506496000, 45047749044458160000, 1335740755933584000000, 41473196779273459200000

OFFSET

3,2

FORMULA

E.g.f.: 1/(1-Sum_{i=1..3} x^i/i!) - 1/(1-Sum_{i=1..2} x^i/i!).

a(n) = A189886(n) - A080599(n).

MAPLE

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

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

end:

a:= n-> (k-> b(n, k) -b(n, k-1))(3):

seq(a(n), n=3..25);

CROSSREFS

Column k=3 of A276922.

Cf. A080599, A189886.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Oct 20 2018

STATUS

approved

editing

#1 by Alois P. Heinz at Sat Oct 20 17:24:21 EDT 2018

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved