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A048742
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n! - n-th Bell number.
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0
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0, 0, 0, 1, 9, 68, 517, 4163, 36180, 341733, 3512825, 39238230, 474788003, 6199376363, 86987391878, 1306291409455, 20912309745853, 355604563226196, 6401691628921841, 121639267666626943, 2432850284018404628, 51090467301893283249, 1123996221061869232677
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Number of permutations of [n] which have at least one cycle that has at least one inversion when written with its smallest element in the first position. Example: a(4)=9 because we have (1)(243), (1432), (142)(3), (132)(4), (1342), (1423), (1243), (143)(2) and (1324). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2008
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LINKS
| Index entries for sequences related to factorial numbers
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MAPLE
| with(combinat): seq(factorial(n)-bell(n), n=0..21); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2008
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MATHEMATICA
| Table[n! - BellB[n], {n, 0, 40}] (* From Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
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PROG
| sage: [factorial(m)-bell_number(m) for m in xrange (0, 23)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008
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CROSSREFS
| A000142 - A000110.
Sequence in context: A002051 A133120 A194650 * A121633 A091708 A024119
Adjacent sequences: A048739 A048740 A048741 * A048743 A048744 A048745
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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