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A111492
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Array, a(n,k) = (k-1)!C(n,k), read by rows.
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0
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1, 2, 1, 3, 3, 2, 4, 6, 8, 6, 5, 10, 20, 30, 24, 6, 15, 40, 90, 144, 120, 7, 21, 70, 210, 504, 840, 720, 8, 28, 112, 420, 1344, 3360, 5760, 5040, 9, 36, 168, 756, 3024, 10080, 25920, 45360, 40320, 10, 45, 240, 1260, 6048, 25200, 86400, 226800, 403200, 362880
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For k > 1, a(n,k) = the number of permutations of the symmetric group S_n that are pure k-cycles.
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FORMULA
| a(n, k) = (k-1)!C(n, k) = P(n, k)/k.
E.g.f. (by columns) = exp(x)((x^k)/k).
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EXAMPLE
| a(3,3) = 2 because (3-1)!C(3,3) = 2.
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MATHEMATICA
| Flatten[Table[(k - 1)!Binomial[n, k], {n, 10}, {k, n}]]
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CROSSREFS
| a(n, 1) = A000027(n); a(n, 2) = A000217(n-1); a(n, 3) = A007290(n); a(n, 4) = A033487(n-3).
a(n, n) = A000142(n-1); a(n, n-1) = A001048(n-1) for n > 1.
Sum[a(n, k), {k, 1, n}] = A002104(n); Sum[a(n, k), {k, 2, n}] = A006231(n).
Sequence in context: A006642 A094435 A133341 * A144305 A138635 A128182
Adjacent sequences: A111489 A111490 A111491 * A111493 A111494 A111495
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KEYWORD
| nonn,tabl
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Nov 15 2005
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