|
|
A320697
|
|
Number of partitions of n with up to ten distinct kinds of 1.
|
|
2
|
|
|
1, 10, 46, 131, 267, 439, 654, 956, 1394, 2002, 2817, 3897, 5320, 7179, 9587, 12687, 16652, 21687, 28048, 36051, 46066, 58534, 73998, 93113, 116649, 145513, 180793, 223800, 276077, 339417, 415942, 508179, 619090, 752128, 911336, 1101444, 1327973, 1597358
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ Pi * 2^(15/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^10 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021
|
|
MAPLE
|
b:= proc(n, i) option remember; `if`(n=0 or i=1,
binomial(10, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|