

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).


LINKS



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])^(n1)/(n!*(n1)!); \\ Michel Marcus, Jun 07 2023


CROSSREFS



KEYWORD

nonn


AUTHOR

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


EXTENSIONS



STATUS

approved



