|
|
A160988
|
|
Number of partitions of n where every part appears at least 18 times
|
|
1
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 7, 7, 8, 7, 10, 8, 10, 10, 11, 10, 15, 12, 14, 15, 17, 15, 19, 17, 20, 20, 21, 20, 25, 22, 24, 25, 27, 25, 32, 28, 32, 32, 34, 34, 39, 35, 39, 40, 43, 40, 46, 43, 47
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,36
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-18*x)) dx = -1.334989118601880353022790449460912585887590533324376464199... . - Vaclav Kotesovec, Jan 05 2016
|
|
MATHEMATICA
|
nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(18*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|