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A101109
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Number of sets of lists (sequences) of n labeled elements with k=3 elements per list.
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1
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1, 0, 0, 6, 0, 0, 360, 0, 0, 60480, 0, 0, 19958400, 0, 0, 10897286400, 0, 0, 8892185702400, 0, 0, 10137091700736000, 0, 0, 15388105201717248000, 0, 0, 30006805143348633600000, 0, 0, 73096577329197271449600000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The (labeled) case for k=2 is A067994, the Hermite numbers. The (labeled) case for k>=1 is A000262, Number of "sets of lists".
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FORMULA
| egf = exp(z^3); In Maple notation: a(n) = n!*PIECEWISE([1/GAMMA(1/3*n+1), irem(n, 3) = 0], [0, irem(n-1, 3) = 0], [0, irem(n-2, 3) = 0]); recurrence: a(0) = 1, a(1) = 0, a(2) = 0, (-n-3)*a(n+3)+3*a(n).
a(n) = n!/(n/3)!, if [3|n], 0 otherwise. - Mitch Harris, Jan 19 2006
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EXAMPLE
| Let Z[i] denote the i-th labeled element. Then a(3) = 6 with the following six sets:
Set(Sequence(Z[3],Z[1],Z[2])), Set(Sequence(Z[2],Z[1],Z[3])), Set(Sequence(Z[3],Z[2],Z[1])), Set(Sequence(Z[2],Z[3],Z[1])), Set(Sequence(Z[1],Z[3],Z[2])), Set(Sequence(Z[1],Z[2],Z[3])).
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MAPLE
| A101109 := n -> n!*PIECEWISE([1/GAMMA(1/3*n+1), irem(n, 3) = 0], [0, irem(n-1, 3) = 0], [0, irem(n-2, 3) = 0]); [ seq(n!*PIECEWISE([1/GAMMA(1/3*n+1), irem(n, 3) = 0], [0, irem(n-1, 3) = 0], [0, irem(n-2, 3) = 0]), n=0..30) ];
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CROSSREFS
| Cf. A000262, A067994.
Sequence in context: A019157 A019184 A019185 * A192072 A060297 A137378
Adjacent sequences: A101106 A101107 A101108 * A101110 A101111 A101112
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (wieder.thomas(AT)t-online.de), Dec 01 2004
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