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A272495 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to five. 2
1, 6, 63, 560, 5922, 61992, 739662, 9086616, 122792670, 1741884144, 26631631026, 428931318816, 7362963616008, 132977285400960, 2538822785931432, 50863863365419104, 1070731366348427784, 23576426902769412672, 542918591829347774040, 13035693339696004705728 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..450

FORMULA

E.g.f.: x^5 * Product_{i=1..5} (i-1)!/(i!-x^i).

MAPLE

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

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

    end:

a:= n-> (k-> b(n, k) -b(n, k-1))(5):

seq(a(n), n=5..30);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i]]]];

a[n_] := b[n, 5] - b[n, 4];

a /@ Range[5, 30] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A262071.

Sequence in context: A267248 A053535 A268220 * A039937 A134112 A071588

Adjacent sequences:  A272492 A272493 A272494 * A272496 A272497 A272498

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified September 25 06:22 EDT 2022. Contains 356959 sequences. (Running on oeis4.)