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Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^10)).
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%I #22 Oct 02 2023 14:27:46

%S 1,2,4,7,12,19,30,45,67,97,139,194,269,366,494,658,870,1137,1477,1900,

%T 2430,3083,3890,4874,6078,7533,9294,11406,13940,16955,20545,24787,

%U 29800,35688,42600,50670,60088,71024,83714,98377,115305,134771,157138,182746,212038

%N Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^10)).

%C Number of partitions of at most n into at most 10 parts.

%H Seiichi Manyama, <a href="/A288345/b288345.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_56">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, 0, -1, 1, -1, 1, 0, 0, -1, 2, 0, 0, 1, -2, 0, -1, 0, 0, 0, -2, 3, 0, 1, 0, 1, 0, -1, 0, -1, 0, -3, 2, 0, 0, 0, 1, 0, 2, -1, 0, 0, -2, 1, 0, 0, -1, 1, -1, 1, 0, 1, 0, -2, 1).

%o (PARI) x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 10, (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), A288344 (k=9), this sequence (k=10).

%Y Cf. A008639 (first differences).

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jun 08 2017