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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
OFFSET
5,2
LINKS
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-François Alcover, Dec 11 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A262071.
Sequence in context: A267248 A053535 A268220 * A039937 A134112 A071588
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2016
STATUS
approved