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 A163176 The n-th Minkowski number divided by the n-th factorial: a(n) = A053657(n)/n!. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS F. Bencherif, Sur une propriété des polynômes de Stirling, 26th Journées Arithmétiques, July 6-10, 2009, Université Jean Monnet, Saint-Etienne, France. Farid Bencherif, Tarek Garici, On a property of Stirling polynomials, Publications de l'Institut Mathématique (2017), Vol. 102, Issue 116, pp. 149-153. J.-L. Chabert, Integer-valued polynomials on prime numbers and logarithm power expansion, European J. Combinatorics 28 (2007) 754-761. FORMULA a(n) = (1/n!)*Prod_{p prime} p^{Sum_{k>=0} [(n-1)/((p-1)p^k)]}. EXAMPLE a(4) = A053657(4)/4! = 48/24 = 2. MAPLE Contribution from Peter Luschny, 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) MATHEMATICA a[n_] := (1/n!)*Product[ p^Sum[ Floor[ (n-1)/((p-1)*p^k) ], {k, 0, n}], {p, Select[ Range[2, n], PrimeQ]}]; Table[ a[n], {n, 1, 27}] (* Jean-François Alcover, Dec 07 2011 *) CROSSREFS Cf. A053657. Sequence in context: A120968 A193894 A107667 * A277306 A201444 A236381 Adjacent sequences:  A163173 A163174 A163175 * A163177 A163178 A163179 KEYWORD easy,nonn AUTHOR Jonathan Sondow, Jul 24 2009 STATUS approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)