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A272494 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to four. 2
1, 5, 45, 350, 3290, 30870, 334950, 3765300, 46950750, 617867250, 8815156350, 133031398500, 2149039893000, 36645888279000, 662781093975000, 12612741639498000, 252857867367105000, 5314211504296695000, 117053051989758885000, 2693288170000578150000 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..450

FORMULA

E.g.f.: x^4 * Product_{i=1..4} (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))(4):

seq(a(n), n=4..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, 4] - b[n, 3];

a /@ Range[4, 30] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A262071.

Sequence in context: A043025 A190540 A268219 * A185009 A125836 A001260

Adjacent sequences:  A272491 A272492 A272493 * A272495 A272496 A272497

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified October 7 10:36 EDT 2022. Contains 357270 sequences. (Running on oeis4.)