|
Search: id:A008485
|
|
|
| A008485 |
|
Coefficient of x^n in Product 1/(1-x^m )^n. |
|
+0
2
|
|
| 1, 5, 22, 105, 506, 2492, 12405, 62337, 315445, 1605340, 8207563, 42124380, 216903064, 1119974875, 5796944357, 30068145905, 156250892610, 813310723925, 4239676354650, 22130265931900, 115654632452535
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Number of partitions of n into parts of n kinds. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 08 2002
|
|
FORMULA
|
a(n) = Sum_{pi} Product_{i=1..n} binomial(k_i+n-1, k_i) where pi runs through all nonnegative solutions of k_1+2*k_2+...+n*k_n=n. a(n) = b(n, n) where b(n, m)= m/n*Sum_{i=1..n} sigma(i)*b(n-i, m) is recurrence for number of partitions of n into parts of m kinds. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 08 2002
|
|
MAPLE
|
with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; `if`(n=0, 1, add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) end end: a:= n-> etr(j->n)(n): seq (a(n), n=1..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008]
|
|
CROSSREFS
|
Cf. A000041, A000712, A000716, A023003-A023021, A005758, A006922.
Sequence in context: A048251 A017971 A017972 this_sequence A082297 A162271 A164593
Adjacent sequences: A008482 A008483 A008484 this_sequence A008486 A008487 A008488
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. Forbes (anthony.d.forbes(AT)googlemail.com)
|
|
|
Search completed in 0.002 seconds
|
