A393516 Number of partitions of n in which (number of odd parts) / (number of even parts) = 3/2.

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, 102, 212, 166, 285, 259, 380, 399, 506, 596, 673, 882, 897, 1275, 1198, 1826, 1605, 2572, 2159, 3591, 2910, 4948, 3935, 6769, 5326, 9164, 7217, 12327, 9772, 16448, 13225, 21826

Offset

0,10

Links

Table of n, a(n) for n=0..58.

Formula

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))) ).

Example

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

Crossrefs

Cf. A393517.

Sequence in context: A326831 A196409 A369909 * A326830 A115333 A242689

Adjacent sequences: A393513 A393514 A393515 * A393517 A393518 A393519

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2026

Status

approved