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Sum of absolute values of coefficients of expansion of (1-x)(1-x^2)(1-x^3)...(1-x^n).
1

%I #19 May 03 2018 16:45:24

%S 1,2,4,6,8,12,16,20,28,36,44,54,72,92,104,138,176,212,268,332,416,508,

%T 628,776,968,1192,1480,1836,2288,2812,3472,4292,5312,6572,8120,10028,

%U 12388,15300,18860,23276,28740,35468,43732,53954,66540,82016,101044

%N Sum of absolute values of coefficients of expansion of (1-x)(1-x^2)(1-x^3)...(1-x^n).

%C a(n) >= A160089(n) with equality only for n=0. - _Michel Marcus_, Jun 12 2013

%H Seiichi Manyama, <a href="/A061553/b061553.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) := |c(n, 0)| + |c(n, 1)| + ... + |c(n, n(n+1)/2)| where c(n, j) are the coefficients of the polynomial P(n, x) := (1-x)(1-x^2)(1-x^3)...(1-x^n)

%e a(1) = 1+1 = 2; a(4) = Length(P(4,x)) = Length(1 - x - x^2 + 2x^5 - x^8 - x^9 + x^10) = 1+1+1+2+1+1+1 = 8

%o (PARI) a(n) = {pol = prod(i=1, n, 1-x^i); return (sum(i=0, poldegree(pol), abs(polcoeff(pol, i))));} \\ _Michel Marcus_, Jun 12 2013

%Y Cf. A160089, A231599.

%K nonn

%O 0,2

%A Steffen Eckmann (steffen.eckmann(AT)eon.com), May 17 2001

%E a(0)=1 prepended by _Seiichi Manyama_, May 03 2018