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).

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