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A304036 Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... .

%I A304036 #22 May 06 2018 03:17:29
%S A304036 1,1,2,1,2,1,3,2,3,1,2,1,3,2,3,1,2,1,3,2,3,1,2,1,4,3,5,2,4,2,5,3,4,1,
%T A304036 2,1,3,2,3,1,2,1,3,2,3,1,2,1,4,3,5,2,4,2,5,3,4,1,2,1,3,2,3,1,2,1,3,2,
%U A304036 3,1,2,1,4,3,5,2,4,2,5,3,4,1,2,1,3,2,3,1,2
%N A304036 Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... .
%H A304036 Seiichi Manyama, <a href="/A304036/b304036.txt">Table of n, a(n) for n = 0..10000</a>
%H A304036 Wikipedia, <a href="http://en.wikipedia.org/wiki/Factoradic">Factorial number system</a>
%F A304036 G.f.: Product_{j>=1} Sum_{k=0..j+1} x^(k*j!) = Product_{j>=1} (1-x^((j+1)!+j!))/(1-x^(j!)).
%e A304036 a(6) = 3 because we have [6], [2,2,2] and [2,2,1,1].
%Y A304036 Cf. A001048, A064986, A303939, A304039.
%K A304036 nonn,look
%O A304036 0,3
%A A304036 _Seiichi Manyama_, May 05 2018