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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
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
Cf. A236810.
Sequence in context: A033520 A210818 A093940 * A224468 A353697 A328364
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Feb 08 2014
EXTENSIONS
a(8)-a(11) from Alois P. Heinz, Feb 08 2014
STATUS
approved