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a(n) is the number of nonzero terms in the expansion of (x-y) * (x^2-y^2) * (x^3-y^3) * ... * (x^n-y^n).
7

%I #27 Aug 02 2024 04:32:47

%S 1,2,4,6,7,12,14,18,25,32,36,42,53,68,64,84,97,108,126,146,161,170,

%T 192,208,229,246,274,300,333,348,372,400,427,468,492,526,561,602,626,

%U 644,691,736,772,826,869,902,930,974,1017,1062,1120,1184,1223,1262,1314,1374,1419,1468,1518,1586,1663,1718,1778,1834,1899,1954,2018

%N a(n) is the number of nonzero terms in the expansion of (x-y) * (x^2-y^2) * (x^3-y^3) * ... * (x^n-y^n).

%C In the definition one can take y=1. - _Emeric Deutsch_, Jan 01 2008

%H Joerg Arndt, <a href="/A086781/b086781.txt">Table of n, a(n) for n = 0..1000</a>

%H Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.37193/CJM.2019.01.01">On some results concerning the polygonal polynomials</a>, Carpathian Journal of Mathematics (2019) Vol. 35, No. 1, 1-11.

%p a:=proc(n) options operator, arrow: nops(expand(product(x^j-y^j,j=1..n))) end proc: seq(a(n),n=0..50); # _Emeric Deutsch_, Jan 01 2008

%t Table[Length[Expand[Times@@(x^Range[n]-1)]],{n,50}] (* _Harvey P. Dale_, Mar 01 2012 *)

%o (PARI) a(n)=#select(w->w, Vec(prod(k=1,n,1-'x^k))); \\ _Joerg Arndt_, Apr 12 2017

%Y Cf. A000124, A086376.

%K nonn

%O 0,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003

%E More terms from _Emeric Deutsch_, Jan 01 2008

%E a(0)=1 prepended by _Alois P. Heinz_, Apr 12 2017