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A145513
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Number of partitions of 10^n into powers of 10.
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4
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1, 2, 12, 562, 195812, 515009562, 10837901390812, 1899421190329234562, 2851206628197445401265812, 37421114946843687272702534859562, 4362395890943439751990308572939648140812
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A179051(10^n); for n>0: a(n) = A179052(10^(n-1)). [From Reinhard Zumkeller, Jun 27 2010]
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..26
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FORMULA
| a(n) = [x^(10^n)] 1/Product_{j>=0}(1-x^(10^j)).
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EXAMPLE
| a(1) = 2, because there are 2 partitions of 10^1 into powers of 10: [1,1,1,1,1,1,1,1,1,1], [10].
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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, 10): seq (a(n), n=0..13);
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CROSSREFS
| Cf. 10th column of A145515, A007318.
Sequence in context: A013173 A013147 A050643 * A002860 A108078 A052129
Adjacent sequences: A145510 A145511 A145512 * A145514 A145515 A145516
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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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