|
%I #26 Oct 02 2023 14:23:20
%S 1,2,4,7,12,19,30,44,64,90,125,169,227,298,388,498,634,797,996,1231,
%T 1513,1844,2235,2689,3221,3833,4542,5353,6284,7341,8547,9907,11447,
%U 13176,15121,17293,19725,22427,25436,28767,32459,36529,41023,45958,51385,57327
%N Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^6)).
%C Number of partitions of at most n into at most 6 parts.
%H Seiichi Manyama, <a href="/A288341/b288341.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>, 2017.
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, 0, -1, 1, -2, 2, 1, 0, 0, 0, -1, -2, 2, -1, 1, 0, 1, 0, -2, 1).
%o (PARI) x='x+O('x^99); Vec(1/((1-x)*prod(i=1, 6, (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), this sequence (k=6), A288342 (k=7), A288343 (k=8), A288344 (k=9), A288345 (k=10).
%Y Cf. A288253. Column 6 of A092905. A001402 (first differences).
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jun 08 2017
|
