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A145514
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Number of partitions of n^n into powers of n, also diagonal of A145515 and A196879.
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3
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1, 1, 4, 23, 1086, 642457, 6188114528, 1226373476385199, 6071277235712979102634, 884267692532264259002637317099, 4362395890943439751990308572939648140812
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..22
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FORMULA
| a(n) = [x^(n^n)] 1/Product_{j>=0}(1-x^(n^j)), n>1.
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EXAMPLE
| a(2) = 4, because there are 4 partitions of 2^2=4 into powers of 2: [1,1,1,1], [1,1,2], [2,2], [4].
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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, n): seq (a(n), n=0..13);
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CROSSREFS
| Cf. A145515, A196879, A007318.
Sequence in context: A130890 A138578 A107765 * A024543 A010294 A169688
Adjacent sequences: A145511 A145512 A145513 * A145515 A145516 A145517
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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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