A027190 - OEIS

A027190

Number of partitions of n into an odd number of parts, the least being 4; also, a(n+4) = number of partitions of n into an even number of parts, each >=4.

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 12, 13, 17, 19, 25, 28, 35, 40, 50, 57, 70, 80, 98, 112, 135, 155, 186, 213, 253, 291, 345, 395, 465, 533, 625, 716, 835, 956, 1113, 1272, 1474, 1684, 1946, 2220, 2558, 2915, 3351, 3814, 4372, 4971, 5688, 6457, 7370, 8359, 9524, 10787

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OFFSET

1,14

LINKS

Table of n, a(n) for n=1..69.

FORMULA

G.f.: x^4 * Sum_{k>=0} x^(8*k)/Product_{j=1..2*k} (1-x^j). - Seiichi Manyama, May 15 2023

CROSSREFS

Cf. A027196.

Sequence in context: A238209 A342096 A210716 * A036824 A108104 A173091

Adjacent sequences: A027187 A027188 A027189 * A027191 A027192 A027193

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Seiichi Manyama, May 15 2023

STATUS

approved