

A169815


a(n) = lcm(1, 2, ..., n)^(n1)/(n!*(n1)!).


0



1, 1, 3, 12, 4500, 9000, 1512630000, 1452124800000, 111152892816000000, 3112280998848000000, 1849326140334157445511936000000, 388358489470173063557506560000000, 1607761625123067582500188167647056604083200000000
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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))^(k1)) c(k1, k).


REFERENCES

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. 11351151, 2008.


LINKS



MATHEMATICA

f[n_] := n (LCM @@ Range@n)^(n  1)/n!^2; Array[f, 15] (* Robert G. Wilson v, May 30 2010 *)


CROSSREFS



KEYWORD

nonn


AUTHOR

Iickho Song (i.song(AT)ieee.org), May 25 2010


EXTENSIONS



STATUS

approved



