A363068 Number of partitions p of n such that (1/5)*max(p) is a part of p.

1, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 59, 73, 94, 117, 148, 181, 228, 277, 344, 418, 514, 621, 762, 917, 1116, 1342, 1624, 1945, 2348, 2803, 3366, 4012, 4798, 5700, 6798, 8052, 9565, 11305, 13383, 15771, 18618, 21880, 25745, 30187, 35414, 41414, 48461, 56531, 65967

Offset

0,9

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Sum_{k>=0} x^(6*k)/Product_{j=1..5*k} (1-x^j).

Example

a(8) = 2 counts these partitions:  521, 5111.

Prog

(PARI) a(n) = sum(k=0, n\6, #partitions(n-6*k, 5*k));

Crossrefs

Cf. A002865, A238479, A363066, A363067.

Cf. A237827, A363047.

Sequence in context: A001402 A008629 A347572 * A238864 A070289 A035961

Adjacent sequences: A363065 A363066 A363067 * A363069 A363070 A363071

Keyword

nonn

Author

Seiichi Manyama, May 16 2023

Status

approved