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
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