A393514 Number of partitions of 2*n having four times as many odd parts as even.

1, 0, 0, 1, 2, 4, 8, 14, 23, 37, 57, 86, 129, 188, 273, 392, 558, 785, 1103, 1532, 2122, 2917, 3993, 5429, 7359, 9908, 13296, 17750, 23609, 31251, 41236, 54167, 70930, 92522, 120313, 155899, 201440, 259425, 333203, 426698, 545017, 694235, 882191, 1118161, 1414032

Offset

0,5

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

a(2*4) counts these 2 partitions: 41111, 32111.

Crossrefs

Cf. A045931, A239258, A393513, A393515.

Sequence in context: A089054 A055291 A091773 * A384889 A107055 A202840

Adjacent sequences: A393511 A393512 A393513 * A393515 A393516 A393517

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2026

Status

approved