A288344 Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^9)).

1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 138, 192, 265, 359, 482, 639, 840, 1092, 1410, 1803, 2291, 2889, 3621, 4508, 5584, 6875, 8424, 10269, 12463, 15055, 18115, 21704, 25910, 30814, 36522, 43137, 50794, 59618, 69774, 81422, 94760, 109984, 127338, 147058, 169438

Offset: 0

Author

Seiichi Manyama, Jun 08 2017

Keywords

• nonn
• easy

Comments

Number of partitions of at most n into at most 9 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, 1, 0, -1, 1, 2, -1, 0, 0, -1, -1, 0, 0, -1, 1, 0, 2, 0, 1, -1, 0, 0, -1, -1, 0, 0, -1, 2, 1, -1, 0, 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), A288343 (k=8), this sequence (k=9), A288345 (k=10).

Cf. A288256, A008638 (first differences).

Programs

PARI

x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 9, (1-x^i)))) \\ Altug Alkan, Mar 28 2018