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%I #24 Oct 02 2023 14:26:25
%S 1,2,4,7,12,19,30,45,67,97,138,192,265,359,482,639,840,1092,1410,1803,
%T 2291,2889,3621,4508,5584,6875,8424,10269,12463,15055,18115,21704,
%U 25910,30814,36522,43137,50794,59618,69774,81422,94760,109984,127338,147058,169438
%N Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^9)).
%C Number of partitions of at most n into at most 9 parts.
%H Seiichi Manyama, <a href="/A288344/b288344.txt">Table of n, a(n) for n = 0..10000</a>
%H Richard J. Mathar, <a href="/A293482/a293482.pdf">Size of the Set of Residues of Integer Powers of Fixed Exponent</a>, research paper, 2017.
%H <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, 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).
%o (PARI) x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 9, (1-x^i)))) \\ _Altug Alkan_, Mar 28 2018
%Y 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).
%Y Cf. A288256, A008638 (first differences).
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jun 08 2017
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