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A320759 Number of ordered set partitions of [n] where the maximal block size equals three. 2
1, 8, 80, 860, 10290, 136080, 1977360, 31365600, 539847000, 10026139200, 199937337600, 4262167509600, 96744738090000, 2329950823200000, 59348032327584000, 1594257675506496000, 45047749044458160000, 1335740755933584000000, 41473196779273459200000 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..424

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);

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-Fran├žois Alcover, Dec 14 2020, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A276922.

Cf. A080599, A189886.

Sequence in context: A346178 A102592 A345081 * A233123 A269796 A328128

Adjacent sequences:  A320756 A320757 A320758 * A320760 A320761 A320762

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2018

STATUS

approved

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)