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%I #9 Feb 22 2019 06:05:14
%S 0,1,1,2,1,3,2,4,3,6,4,7,6,9,8,11,10,14,13,17,16,20,20,24,24,28,28,34,
%T 33,39,39,45,45,52,52,59,59,68,67,76,76,86,86,96,97,108,108,121,121,
%U 134,135,149,150,164,166,182,183,200,202,220,222,241,244,263,267,288,291,313,317
%N Number of partitions of n into Catalan numbers A000108 where every part appears at least 2 times.
%H R. H. Hardin, <a href="/A161227/b161227.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: -1 + Product_{j>=1} (1 + x^(2*binomial(2j,j)/(j+1))/(1-x^(binomial(2j,j)/(j+1)))). - _Emeric Deutsch_, Jun 22 2009
%e a(10)=6 because we have 55, 22222, 222211, 2221111, 22111111, and 1^(10). - _Emeric Deutsch_, Jun 22 2009
%p g := -1+product(1+x^(2*binomial(2*j, j)/(j+1))/(1-x^(binomial(2*j, j)/(j+1))), j = 1 .. 10): gser := series(g, x = 0, 75): seq(coeff(gser, x, n), n = 1 .. 70); # _Emeric Deutsch_, Jun 22 2009
%K nonn
%O 1,4
%A _R. H. Hardin_, Jun 06 2009
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