A393517 Number of partitions of 2*n in which (number of odd parts) / (number of even parts) = 2/3.

1, 0, 0, 0, 1, 2, 5, 9, 17, 27, 44, 66, 101, 146, 214, 303, 434, 607, 855, 1184, 1649, 2266, 3121, 4256, 5808, 7856, 10621, 14254, 19101, 25434, 33798, 44661, 58883, 77251, 101099, 131738, 171240, 221719, 286385, 368626, 473364, 605956, 773930, 985643, 1252557, 1587594

Offset

0,6

Links

Table of n, a(n) for n=0..45.

Formula

G.f.: Sum_{k>=0} x^(4*k) / ( (Product_{j=1..2*k} (1-x^j)) * (Product_{j=1..3*k} (1-x^j)) ).

Example

a(2*5) counts these 2 partitions: 42211, 32221.

Crossrefs

Cf. A393516.

Sequence in context: A165271 A308827 A139672 * A308873 A308933 A308998

Adjacent sequences: A393514 A393515 A393516 * A393518 A393519 A393520

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2026

Status

approved