|
%I #23 Oct 08 2017 23:47:12
%S 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,
%T 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,
%U 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
%N Number of partitions of n into distinct factorials.
%C a(A115944(n)) > 0; a(A115944(n)) = 0;
%C a(A115647(n)) > 0;
%C what is the smallest n such that a(n) > 1?.
%C No such n exists as 0 <= a(n) <= 1, cf. formula;
%C a(A059590(n)) = 1. - _Reinhard Zumkeller_, Dec 04 2011
%H Reinhard Zumkeller, <a href="/A115944/b115944.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F G.f.: Product_{j>=1} (1 + x^(j!)). - _Emeric Deutsch_, Apr 06 2006
%F a(n! + k) = a(k) for k: 0 <= k < (n-1)! and a(n! + k)=0 for k: (n-1)! <= k < n!.
%F a(n! + k) = 0 for k: (n-1)! <= k < n!.
%e a(32)=1 because we have [24,6,2].
%p 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
%t 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_ *)
%o (Haskell)
%o a115944 = p (tail a000142_list) where
%o p _ 0 = 1
%o p (f:fs) m | m < f = 0
%o | otherwise = p fs (m - f) + p fs m
%o -- _Reinhard Zumkeller_, Dec 04 2011
%Y Cf. A064986.
%Y Cf. A197183.
%K nonn
%O 0
%A _Reinhard Zumkeller_, Feb 02 2006
%E Offset changed and initial a(0)=1 added by _Reinhard Zumkeller_, Dec 04 2011
|
