A288343 Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^8)).

1, 2, 4, 7, 12, 19, 30, 45, 67, 96, 136, 188, 258, 347, 463, 609, 795, 1025, 1313, 1665, 2099, 2624, 3262, 4026, 4945, 6035, 7332, 8859, 10660, 12764, 15226, 18083, 21402, 25230, 29647, 34713, 40525, 47155, 54719, 63307, 73056, 84074, 96524, 110536, 126301

Offset: 0

Author

Seiichi Manyama, Jun 08 2017

Keywords

• nonn
• easy

Comments

Number of partitions of at most n into at most 8 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, 2017.
• Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, 0, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -2, 0, -1, 1, 0, 2, -1, 1, 1, -1, -1, -1, 1, -1, 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), A288342 (k=7), this sequence (k=8), A288344 (k=9), A288345 (k=10).

Cf. A288255.

Programs

Mathematica

CoefficientList[Series[1/((1-x)Times@@(1-x^Range[8])),{x,0,50}],x] (* Harvey P. Dale, Dec 06 2017 *)

PARI

x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 8, (1-x^i)))) \\ Altug Alkan, Mar 28 2018