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%I #7 Feb 18 2026 08:14:05
%S 1,0,0,0,1,2,5,9,17,27,44,66,101,146,214,303,434,607,855,1184,1649,
%T 2266,3121,4256,5808,7856,10621,14254,19101,25434,33798,44661,58883,
%U 77251,101099,131738,171240,221719,286385,368626,473364,605956,773930,985643,1252557,1587594
%N Number of partitions of 2*n in which (number of odd parts) / (number of even parts) = 2/3.
%F G.f.: Sum_{k>=0} x^(4*k) / ( (Product_{j=1..2*k} (1-x^j)) * (Product_{j=1..3*k} (1-x^j)) ).
%e a(2*5) counts these 2 partitions: 42211, 32221.
%Y Cf. A393516.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Feb 18 2026