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Search: id:A086363
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| A086363 |
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Array T(m,n) read by antidiagonals: if X and Y are two (possibly empty) finite sets with m and n elements respectively, and Z is the disjoint union of X and Y, then T(m,n) is the number of self inverse partial functions f:Z ->Z which do not fix any element of Y. |
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+0
1
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| 1, 1, 2, 2, 3, 5, 4, 6, 9, 14, 190, 14, 20, 29, 43
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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T(m, n)=T(m, n-1)+m*T(m-1, n-1)+(n-1)*T(m, n-2) for m>0, n>1; T(m, 0)=b(m); T(m, 1)=b(m)+m*b(m-1); T(0, n)=c(n); where sequences b and c are A005425 and A000085 respectively.
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EXAMPLE
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E.g. T(1,2)=6: If we let X={1}, Y={2,3}, so Z={1,2,3} and the relevant partial functions f:Z ->Z which do not fix either 2 or 3 are (-,-,-), (1,-,-), (-,3,2), (1,3,2), (2,1,-), (3,-,1). Here a partial function f:Z ->Z is displayed as (f(1),f(2),f(3)).
Array begins:
1 1 2 4 10 26 76 232 764...
2 3 6 14 36 102 308 996 3384...
5 9 20 50 138 410 1304 4380 15500...
14 29 70 188 548 1714 5684 19880 72808...
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CROSSREFS
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Adjacent sequences: A086360 A086361 A086362 this_sequence A086364 A086365 A086366
Sequence in context: A036716 A026399 A117267 this_sequence A139171 A050174 A115126
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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James East (jameseastseq(AT)hotmail.com), Sep 04 2003
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