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A272500
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Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to ten.
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2
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1, 11, 198, 2860, 47047, 738738, 12828816, 223282488, 4179020274, 80464009340, 1640551617848, 34682405557800, 770529476530814, 17782248154604934, 428864975324828328, 10740325059575465640, 279932748231053890830, 7564798231253861700960, 212075260563875086898520
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OFFSET
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10,2
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LINKS
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FORMULA
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E.g.f.: x^10 * Product_{i=1..10} (i-1)!/(i!-x^i).
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MAPLE
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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))(10):
seq(a(n), n=10..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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