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A111903
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The work performed by a partial function f:{1,...,n}->{1,...,n} is defined to be work(f)=sum(|i-f(i)|,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all order-preserving partial functions f:{1,...,n}->{1,...,n}.
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3
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0, 4, 48, 424, 3312, 24204, 169632, 1155152, 7702944, 50550932, 327591504, 2101442808, 13367744784, 84438657820, 530179314240, 3311794268320, 20594613427776, 127564892050212, 787394746252656
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| James East The Work Performed by a Transformation Semigroup, preprint 2005.
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FORMULA
| Sum(i, j=1...n;k, l=0...n, |i-j|*(i-1 choose k)*(j+k-1 choose k)*(n-i choose l)*(n-j+l choose l))
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EXAMPLE
| When n=2 there are 8 order-preserving partial maps {1,2}->{1,2}. these are (1 2), (1 1), (2 2), (1 -), (2 -), (- 1), (- 2) (- -). Adding up the work performed by these maps (from left to right as arranged above) gives a(2)=0+1+1+0+1+1+0+0=4.
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CROSSREFS
| Cf. A111867, A111873, A111874.
Sequence in context: A091904 A192831 A158681 * A059409 A026942 A159903
Adjacent sequences: A111900 A111901 A111902 * A111904 A111905 A111906
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KEYWORD
| easy,nonn
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AUTHOR
| James East (jameseastseq(AT)hotmail.com), Nov 23 2005
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