|
| |
|
|
A096914
|
|
Number of partitions of 2*n into distinct parts with exactly two odd parts.
|
|
3
|
|
|
|
1, 2, 4, 7, 11, 17, 25, 36, 50, 69, 93, 124, 163, 212, 273, 349, 442, 556, 695, 863, 1066, 1310, 1602, 1950, 2364, 2854, 3433, 4115, 4916, 5854, 6951, 8229, 9716, 11442, 13441, 15752, 18419, 21490, 25021, 29074, 33718, 39031, 45101, 52024, 59910
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,2
|
|
|
LINKS
|
Table of n, a(n) for n=2..46.
|
|
|
FORMULA
|
G.f. for number of partitions of n into distinct parts with exactly k odd parts is x^(k^2)*Product(1+x^(2*m), m=1..infinity)/Product(1-x^(2*m), m=1..k).
a(n) ~ 3^(3/4) * exp(Pi*sqrt(n/3)) * n^(1/4) / (2*Pi^2). - Vaclav Kotesovec, May 29 2018
|
|
|
MATHEMATICA
|
Drop[ Union[ CoefficientList[ Series[x^4* Product[1 + x^(2m), {m, 1, 50}] / Product[1 - x^(2m), {m, 1, 2}], {x, 0, 920}], x]], 1] (* Robert G. Wilson v, Aug 21 2004 *)
nmax = 50; Drop[CoefficientList[Series[(x^2/(1 - x - x^2 + x^3)) * Product[1 + x^m, {m, 1, nmax}], {x, 0, nmax}], x], 2] (* Vaclav Kotesovec, May 29 2018 *)
|
|
|
CROSSREFS
|
Cf. A000009, A036469, A015128.
Sequence in context: A034379 A007000 A073472 * A004250 A289060 A194805
Adjacent sequences: A096911 A096912 A096913 * A096915 A096916 A096917
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Vladeta Jovovic, Aug 18 2004
|
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v, Aug 21 2004
|
|
|
STATUS
|
approved
|
| |
|
|
