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 A169815 a(n) = lcm(1, 2, ..., n)^(n-1)/(n!*(n-1)!). 0
 1, 1, 3, 12, 4500, 9000, 1512630000, 1452124800000, 111152892816000000, 3112280998848000000, 1849326140334157445511936000000, 388358489470173063557506560000000, 1607761625123067582500188167647056604083200000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Consider a natural number n. Let t(k) denote the least common multiple (LCM) of {1, 2, ..., k} and Q(t(k)) denote the quotient of n when divided by t(k). Then the number M(n,k) of partitions of n with k parts can be expressed as a polynomial in Q(t(k)) with the leading coefficient (that is, the coefficient of Q(t(k))^(k-1)) c(k-1, k). LINKS Table of n, a(n) for n=1..13. S. R. Park, J. Bae, H. G. Kang and I. Song, On the polynomial representation for the number of partitions with fixed length, Mathematics of Computation, vol. 77, no. 262, pp. 1135-1151, 2008. MATHEMATICA f[n_] := n (LCM @@ Range@n)^(n - 1)/n!^2; Array[f, 15] (* Robert G. Wilson v, May 30 2010 *) PROG (PARI) a(n) = lcm([1..n])^(n-1)/(n!*(n-1)!); \\ Michel Marcus, Jun 07 2023 CROSSREFS Sequence in context: A216897 A262541 A036300 * A239891 A226129 A167368 Adjacent sequences: A169812 A169813 A169814 * A169816 A169817 A169818 KEYWORD nonn AUTHOR Iickho Song (i.song(AT)ieee.org), May 25 2010 EXTENSIONS a(9) onwards from Robert G. Wilson v, May 30 2010 STATUS approved

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Last modified April 22 15:04 EDT 2024. Contains 371905 sequences. (Running on oeis4.)