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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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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; refs; listen; history; internal format)
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OFFSET
| 0,6
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..675
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FORMULA
| 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
| 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
| 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
| Cf. A006231(first column), A000276, A000483, A124324.
Sequence in context: A147437 A147369 A066480 * A145372 A145373 A088577
Adjacent sequences: A136391 A136392 A136393 * A136395 A136396 A136397
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), May 03 2008
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