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A272499
Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to nine.
2
1, 10, 165, 2200, 33605, 492492, 8018010, 131342640, 2321677930, 42349478600, 820275716546, 16515429370440, 350240612952230, 7731410818511380, 178693701272340540, 4296129057927296304, 107666415418378051950, 2801776425029317564400, 75741144900761549630850
OFFSET
9,2
LINKS
FORMULA
E.g.f.: x^9 * Product_{i=1..9} (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))(9):
seq(a(n), n=9..30);
CROSSREFS
Column k=9 of A262071.
Sequence in context: A064747 A285995 A278096 * A305604 A367444 A054688
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2016
STATUS
approved