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A115944
Number of partitions of n into distinct factorials.
17
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
OFFSET
0
COMMENTS
a(A115944(n)) > 0; a(A115944(n)) = 0;
a(A115647(n)) > 0;
what is the smallest n such that a(n) > 1?.
No such n exists as 0 <= a(n) <= 1, cf. formula;
a(A059590(n)) = 1. - Reinhard Zumkeller, Dec 04 2011
FORMULA
G.f.: Product_{j>=1} (1 + x^(j!)). - Emeric Deutsch, Apr 06 2006
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!.
EXAMPLE
a(32)=1 because we have [24,6,2].
MAPLE
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
MATHEMATICA
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 *)
PROG
(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
-- Reinhard Zumkeller, Dec 04 2011
CROSSREFS
Cf. A064986.
Cf. A197183.
Sequence in context: A285498 A285504 A130093 * A166446 A103368 A055132
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 02 2006
EXTENSIONS
Offset changed and initial a(0)=1 added by Reinhard Zumkeller, Dec 04 2011
STATUS
approved