A393516 - OEIS

%I #8 Feb 18 2026 08:14:11

%S 1,0,0,0,0,0,0,1,0,2,0,5,0,9,1,16,2,25,5,39,10,57,20,82,35,114,62,157,

%T 102,212,166,285,259,380,399,506,596,673,882,897,1275,1198,1826,1605,

%U 2572,2159,3591,2910,4948,3935,6769,5326,9164,7217,12327,9772,16448,13225,21826

%N Number of partitions of n in which (number of odd parts) / (number of even parts) = 3/2.

%F G.f.: Sum_{k>=0} x^(7*k) / ( (Product_{j=1..2*k} (1-x^(2*j))) * (Product_{j=1..3*k} (1-x^(2*j))) ).

%e a(9) counts these 2 partitions: 42111, 32211.

%Y Cf. A393517.

%K nonn

%O 0,10

%A _Seiichi Manyama_, Feb 18 2026