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A008485
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Coefficient of x^n in Product 1/(1-x^m )^n.
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2
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1, 5, 22, 105, 506, 2492, 12405, 62337, 315445, 1605340, 8207563, 42124380, 216903064, 1119974875, 5796944357, 30068145905, 156250892610, 813310723925, 4239676354650, 22130265931900, 115654632452535
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of partitions of n into parts of n kinds. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 08 2002
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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
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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]
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CROSSREFS
| Cf. A000041, A000712, A000716, A023003-A023021, A005758, A006922.
Sequence in context: A048251 A017971 A017972 * A082297 A162271 A164593
Adjacent sequences: A008482 A008483 A008484 * A008486 A008487 A008488
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KEYWORD
| nonn
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AUTHOR
| T. Forbes (anthony.d.forbes(AT)googlemail.com)
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