|
| |
|
|
A270995
|
|
Expansion of Product_{k>=1} 1/(1 - A000009(k)*x^k).
|
|
36
|
|
|
|
1, 1, 2, 4, 7, 12, 23, 37, 64, 108, 180, 290, 488, 772, 1251, 2001, 3180, 4982, 7913, 12261, 19162, 29669, 45804, 70187, 108029, 164276, 250267, 379439, 574067, 864044, 1302169, 1949050, 2917900, 4352796, 6481627, 9620256, 14274080, 21090608, 31142909
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
The number of ways a number can be partitioned into not necessarily distinct parts and then each part is partitioned into distinct parts. Also a(n) > A089259(n) for n>5. - Gus Wiseman, Apr 10 2016
|
|
|
LINKS
|
Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
Vaclav Kotesovec, Graph - The asymptotic ratio (100000 terms)
|
|
|
FORMULA
|
From Vaclav Kotesovec, Mar 28 2016: (Start)
a(n) ~ c * n^2 * 2^(n/3), where
c = 436246966131366188.9451742926272200575837456478739... if mod(n,3) = 0
c = 436246966131366188.9351143199611598469443841182807... if mod(n,3) = 1
c = 436246966131366188.9322714926383227135786894927498... if mod(n,3) = 2
(End)
|
|
|
EXAMPLE
|
a(6)=23: {(6), (5)(1), (51), (4)(2), (42), (4)(1)(1), (41)(1), (3)(3), (3)(2)(1), (3)(21), (32)(1), (31)(2), (21)(3), (321), (3)(1)(1)(1), (31)(1)(1), (2)(2)(2), (2)(2)(1)(1), (21)(2)(1), (21)(21), (2)(1)(1)(1)(1), (21)(1)(1)(1), (1)(1)(1)(1)(1)(1)}.
|
|
|
MATHEMATICA
|
nmax = 50; CoefficientList[Series[Product[1/(1-PartitionsQ[k]*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
|
|
|
CROSSREFS
|
Cf. A063834 (twice partitioned numbers), A089259, A271619, A327554, A327608.
Sequence in context: A135360 A347017 A082548 * A299023 A007323 A099604
Adjacent sequences: A270992 A270993 A270994 * A270996 A270997 A270998
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Vaclav Kotesovec, Mar 28 2016
|
|
|
STATUS
|
approved
|
| |
|
|
