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Search: id:A136394
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| A136394 |
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Triangle read by rows: T(n,k) is the number of permutations of an n-set having k cycles of size > 1 (0<=k<=floor(n/2)). |
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+0
1
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| 1, 1, 1, 1, 1, 5, 1, 20, 3, 1, 84, 35, 1, 409, 295, 15, 1, 2365, 2359, 315, 1, 16064, 19670, 4480, 105, 1, 125664, 177078, 56672, 3465, 1, 1112073, 1738326, 703430, 74025, 945, 1, 10976173, 18607446, 8941790, 1346345, 45045, 1, 119481284, 216400569, 118685336
(list; graph; listen)
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OFFSET
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0,6
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..675
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FORMULA
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E.g.f.: exp(x*(1-y))/(1-x)^y. Binomial transform of triangle A008306. exp(x)*((-x-ln(1-x))^k)/k! is e.g.f. of k-th column.
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EXAMPLE
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1;
1;
1,1;
1,5;
1,20,3;
1,84,35;
1,409,295,15;
1,2365,2359,315;
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MAPLE
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egf := proc(k::nonnegint) option remember; x-> exp(x)* ((-x-ln(1-x))^k)/k! end; T := (n, k)-> coeff (series (egf(k)(x), x=0, n+1), x, n) *n!; seq (seq (T(n, k), k=0..floor(n/2)), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008]
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CROSSREFS
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Cf. A006231(first column), A000276, A000483, A124324.
Adjacent sequences: A136391 A136392 A136393 this_sequence A136395 A136396 A136397
Sequence in context: A147437 A147369 A066480 this_sequence A145372 A145373 A088577
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), May 03 2008
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