OFFSET
0,3
COMMENTS
The number of partitions of n into distinct parts where each part can be colored in n different ways. For example, there are 4 partitions of 6 into distinct parts, namely 6, 5 + 1, 4 + 2 and 3 + 2 + 1; allowing for the colorings gives a(6) = 6 + 6*6 + 6*6 + 6*6*6 = 294. - Peter Bala, Aug 31 2017
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..2000 from Robert Israel)
FORMULA
a(n) = A286957(n,n).
a(n) == 0 (mod n); a(n) == n (mod n^2). - Peter Bala, Aug 31 2017
Conjecture: a(n) ~ exp(sqrt(2*(log(n)^2 + Pi^2/3)*n)) * (log(n)^2 + Pi^2/3)^(1/4) / (sqrt(Pi) * (2*n)^(5/4)). - Vaclav Kotesovec, Sep 15 2017
MAPLE
seq(coeff(mul(1+n*x^k, k=1..n), x, n), n=0..50); # Robert Israel, Aug 30 2017
MATHEMATICA
Table[SeriesCoefficient[Product[1 + n x^k, {k, 1, n}], {x, 0, n}], {n, 0, 32}]
Table[SeriesCoefficient[QPochhammer[-n, x]/(1 + n), {x, 0, n}], {n, 0, 32}]
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Ilya Gutkovskiy, Aug 30 2017
STATUS
approved