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Search: id:A163176
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| A163176 |
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The n-th Minkowski number divided by the n-th factorial: a(n) = A053657(n)/n!. |
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+0
5
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| 1, 1, 4, 2, 48, 16, 576, 144, 3840, 768, 9216, 1536, 3870720, 552960, 442368, 55296, 26542080, 2949120, 2229534720, 222953472, 70071091200, 6370099200, 76441190400, 6370099200, 16694755983360, 1284211998720, 570760888320
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is an integer by Legendre's formula for the exponent of the highest power of a prime dividing n!.
a(2n-1) = n*a(2n) because A053657(2n) = 2*A053657(2n-1).
See A053657 for additional comments, references, and links.
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REFERENCES
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J.-L. Chabert, Integer-valued polynomials on prime numbers and logarithm power expansion, European J. Combinatorics 28 (2007) 754-761.
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LINKS
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F. Bencherif, Sur une propriete des polynomes de Stirling
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FORMULA
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a(n) = (1/n!)*Prod_{p prime} p^{Sum_{k>=0} [(n-1)/((p-1)p^k)]}.
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EXAMPLE
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a(4) = A053657(4)/4! = 48/24 = 2.
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MAPLE
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Contribution from Peter Luschny (peter(AT)luschny.de), Jul 26 2009: (Start)
A163176 := proc(n) local L, p;
L := proc(n, p, r) local q, s; q := p-r; s := 0;
do if q > n then break fi; s := s+iquo(n, q);
q := q*p od; s end; mul(p^(L(n-1, p, 1)-L(n, p, 0)),
p = select(isprime, [$2..n])) end: (End)
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CROSSREFS
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Cf. A053657.
Sequence in context: A123850 A120968 A107667 this_sequence A010319 A057167 A096683
Adjacent sequences: A163173 A163174 A163175 this_sequence A163177 A163178 A163179
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jul 24 2009
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