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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
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
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.)