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A115944
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Number of partitions of n into distinct factorials.
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17
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1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0
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COMMENTS
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what is the smallest n such that a(n) > 1?.
No such n exists as 0 <= a(n) <= 1, cf. formula;
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LINKS
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FORMULA
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a(n! + k) = a(k) for k: 0 <= k < (n-1)! and a(n! + k)=0 for k: (n-1)! <= k < n!.
a(n! + k) = 0 for k: (n-1)! <= k < n!.
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EXAMPLE
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a(32)=1 because we have [24,6,2].
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MAPLE
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g:=product(1+x^(j!), j=1..7): gser:=series(g, x=0, 125): seq(coeff(gser, x, n), n=1..122); # Emeric Deutsch, Apr 06 2006
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MATHEMATICA
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max = 7; f[x_] := Product[ 1+x^(j!), {j, 1, max}]; A115944 = Take[ CoefficientList[ Series[ f[x], {x, 0, max!}], x], 106] (* Jean-François Alcover, Dec 28 2011, after Emeric Deutsch *)
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PROG
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(Haskell)
a115944 = p (tail a000142_list) where
p _ 0 = 1
p (f:fs) m | m < f = 0
| otherwise = p fs (m - f) + p fs m
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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