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A064986
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Number of partitions of n into factorial parts ( 0! not allowed ).
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5
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1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 9, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 30, 30, 36, 36, 42, 42, 48, 48, 56, 56, 64, 64, 72, 72, 82, 82, 92, 92, 102, 102, 114, 114, 126, 126, 138, 138, 153, 153, 168, 168, 183, 183, 201, 201, 219, 219, 237, 237, 258, 258, 279, 279
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(2*n+1) = a(2*n) = A117930(n). [Reinhard Zumkeller, Dec 04 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..250
Index entries for sequences related to factorial numbers
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FORMULA
| G.f.: 1/Product_{i=1..infinity} (1-x^(i!)).
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EXAMPLE
| a(3)=2 because we can write 3 = 2!+1! = 1!+1!+1!.
a(3)=2 because we can write 3 = 2!+1! = 1!+1!+1!. And a(10) = 9 because 10 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 = 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 = 1 + 1 + 1 + 1 + 2 + 2 + 2 = 1 + 1 + 2 + 2 + 2 + 2 = 2 + 2 + 2 + 2 + 2 = 1 + 1 + 1 + 1 + 6 = 1 + 1 + 2 + 6 = 2 + 2 + 6.
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PROG
| (Haskell)
a064986 = p (tail a000142_list) where
p _ 0 = 1
p fs'@(f:fs) m | m < f = 0
| otherwise = p fs' (m - f) + p fs m
-- Reinhard Zumkeller, Dec 04 2011
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CROSSREFS
| Cf. A000142, A064985.
Cf. A115944.
Cf. A197182.
Sequence in context: A121260 A121261 A085885 * A029019 A040039 A008667
Adjacent sequences: A064983 A064984 A064985 * A064987 A064988 A064989
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KEYWORD
| easy,nonn
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Oct 30 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs) and Don Reble (djr(AT)nk.ca), Nov 02 2001
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