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A145512
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Number of partitions of 9^n into powers of 9.
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2
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1, 2, 11, 416, 106121, 184174976, 2301962201813, 215628573640652084, 155675227490715893806397, 884267692532264259002637317099, 40145668231846724902431764046045910334
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..27
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FORMULA
| a(n) = [x^(9^n)] 1/Product_{j>=0}(1-x^(9^j)).
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EXAMPLE
| a(1) = 2, because there are 2 partitions of 9^1 into powers of 9: [1,1,1,1,1,1,1,1,1], [9].
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MAPLE
| g:= proc(b, n, k) option remember; local t; if b<0 then 0 elif b=0 or n=0 or k<=1 then 1 elif b>=n then add (g(b-t, n, k) *binomial (n+1, t) *(-1)^(t+1), t=1..n+1); else g(b-1, n, k) +g(b*k, n-1, k) fi end: a:= n-> g(1, n, 9): seq (a(n), n=0..13);
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CROSSREFS
| Cf. 9th column of A145515, A007318.
Sequence in context: A185122 A198894 A015180 * A013046 A012950 A012979
Adjacent sequences: A145509 A145510 A145511 * A145513 A145514 A145515
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008
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