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A087854
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Triangle read by rows: T(n,k) is the number of n-bead necklaces with exactly k different colored beads.
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1
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1, 1, 1, 1, 2, 2, 1, 4, 9, 6, 1, 6, 30, 48, 24, 1, 12, 91, 260, 300, 120, 1, 18, 258, 1200, 2400, 2160, 720, 1, 34, 729, 5106, 15750, 23940, 17640, 5040, 1, 58, 2018, 20720, 92680, 211680, 258720, 161280, 40320, 1, 106, 5613, 81876, 510312, 1643544
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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FORMULA
| T(n, k) = Sum_ {i = 0..., (k-1)} (-1)^i * binomial (k, i) = * A075195(n, k-1); A075195 = Jablonski's table.
T(n, k) = (k!/n) * Sum_{d divides n} phi(d) * S2(n/d, k); = S2(n, k) = Stirling numbers of 2nd kind A008277.
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EXAMPLE
| 1, 0, 0, 0, 0, 0,...
1, 1, 0, 0, 0, 0,...
1, 2, 2, 0, 0, 0, ...
1, 4, 9, 6, 0, 0,...
1, 6, 30, 48, 24, 0, ...
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CROSSREFS
| Columns 1-6 : A000012 A052823 A056283 A056284 A056285 A056286. Diagonals A000142 and A074143. Row sums : apparently A019536.
Cf. Euler totient function phi A000010, A075195 = (Table of Jablonski), A008277 (Stirling 2 numbers).
Sequence in context: A084606 A137399 A158985 * A185041 A086873 A101560
Adjacent sequences: A087851 A087852 A087853 * A087855 A087856 A087857
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| DELEHAM Philippe ( kolotoko(AT)wanadoo.fr)
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