A169815 a(n) = lcm(1, 2, ..., n)^(n-1)/(n!*(n-1)!).

1, 1, 3, 12, 4500, 9000, 1512630000, 1452124800000, 111152892816000000, 3112280998848000000, 1849326140334157445511936000000, 388358489470173063557506560000000, 1607761625123067582500188167647056604083200000000

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).

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. 1135-1151, 2008.

Links

Table of n, a(n) for n=1..13.

Mathematica

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

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