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A272492
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Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to two.
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2
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1, 3, 18, 90, 630, 4410, 37800, 340200, 3515400, 38669400, 471517200, 6129723600, 86497210800, 1297458162000, 20841060240000, 354298024080000, 6389869069584000, 121407512322096000, 2430526127309280000, 51041048673494880000, 1123451899297247520000
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OFFSET
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2,2
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LINKS
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FORMULA
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E.g.f.: x^2 * Product_{i=1..2} (i-1)!/(i!-x^i).
Recurrence: 2*a(n) = 2*n*a(n-1) + (n-1)*n*a(n-2) - (n-2)*(n-1)*n*a(n-3). - Vaclav Kotesovec, May 07 2016
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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))(2):
seq(a(n), n=2..30);
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MATHEMATICA
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Table[n!*(1 + ((-1)^n*(Sqrt[2] - 1) - Sqrt[2] - 1)/2^(n/2 + 1)), {n, 2, 20}] (* Vaclav Kotesovec, May 07 2016 *)
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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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