A288342 Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^7)).

1, 2, 4, 7, 12, 19, 30, 45, 66, 94, 132, 181, 246, 328, 433, 564, 728, 929, 1177, 1477, 1841, 2277, 2799, 3417, 4150, 5010, 6019, 7194, 8561, 10140, 11964, 14057, 16457, 19195, 22315, 25854, 29865, 34391, 39493, 45224, 51654, 58844, 66877, 75823, 85776, 96820

Offset: 0

Author

Seiichi Manyama, Jun 08 2017

Keywords

• nonn
• easy

Comments

Number of partitions of at most n into at most 7 parts.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Richard J. Mathar, Size of the Set of Residues of Integer Powers of Fixed Exponent, research paper, 2017.
• Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, 0, -1, 1, -1, 0, 1, 1, 0, 1, -2, 0, 0, -2, 1, 0, 1, 1, 0, -1, 1, -1, 0, -1, 0, 2, -1).

Crossrefs

Number of partitions of at most n into at most k parts: A002621 (k=4), A002622 (k=5), A288341 (k=6), this sequence (k=7), A288343 (k=8), A288344 (k=9), A288345 (k=10).

Cf. A288254.

Programs

PARI

x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 7, (1-x^i)))) \\ Altug Alkan, Mar 28 2018