|
|
A237512
|
|
Number of solutions to Sum_{k=1..n} k*c(k) = n! , c(k) > 0.
|
|
6
|
|
|
0, 1, 0, 1, 47, 55496, 2080571733, 4441900888487987, 849835826032526606030103, 20540228659655619974131131927286681, 82853643094578125257400348993596774353069331199, 70898139566455107685443806945119782661588205935442233026505921
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
a(n) is the number of partitions of n! - n*(n+1)/2 into parts that are at most n. - Alois P. Heinz, Feb 08 2014
|
|
LINKS
|
|
|
FORMULA
|
a(n) = [x^(n!)] Product_{k=1..n} x^k/(1-x^k).
a(n) = [x^(n!-n*(n+1)/2)] Product_{k=1..n} 1/(1-x^k). - Alois P. Heinz, Feb 08 2014
a(n) ~ n * (n!)^(n-3) ~ n^(n^2-5*n/2-1/2) * (2*Pi)^((n-3)/2) / exp(n*(n-3)-1/12). - Vaclav Kotesovec, Jun 05 2015
|
|
MATHEMATICA
|
Table[Coefficient[Series[Product[x^k/(1-x^k), {k, n}], {x, 0, n!}], x^(n!) ] , {n, 7}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|