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A303506 G.f.: Sum_{n>=1} (-1)^(n-1) * x^(n^2)/(1 - x^n)^n.

%I A303506 #8 Jan 22 2025 11:40:18
%S A303506 1,1,1,0,1,-1,1,-2,2,-3,1,-1,1,-5,7,-7,1,3,1,-12,16,-9,1,1,2,-11,29,
%T A303506 -32,1,28,1,-49,46,-15,16,-18,1,-17,67,-67,1,53,1,-140,162,-21,1,-103,
%U A303506 2,103,121,-244,1,55,211,-305,154,-27,1,-17,1,-29,219,-486,496,-73,1,-592,232,766,1,-931,1,-35,1278,-852,211,-529,1,322,327,-39,1,-1654,1821,-41,379,-1492,1,750,925,-1584
%N A303506 G.f.: Sum_{n>=1} (-1)^(n-1) * x^(n^2)/(1 - x^n)^n.
%H A303506 Antti Karttunen, <a href="/A303506/b303506.txt">Table of n, a(n) for n = 1..20000</a>
%F A303506 a(n) = Sum_{d|n} binomial(n/d-1, d-1) * (-1)^(d-1) for n>=1.
%e A303506 G.f.: A(x) = x + x^2 + x^3 + x^5 - x^6 + x^7 - 2*x^8 + 2*x^9 - 3*x^10 + x^11 - x^12 + x^13 - 5*x^14 + 7*x^15 - 7*x^16 + x^17 + 3*x^18 + ...
%e A303506 such that
%e A303506 A(x) = x/(1-x) - x^4/(1-x^2)^2 + x^9/(1-x^3)^3 - x^16/(1-x^4)^4 + x^25/(1-x^5)^5 - x^36/(1-x^6)^6 + x^49/(1-x^7)^7 - x^64/(1-x^8)^8 +...
%o A303506 (PARI) {a(n) = sumdiv(n,d, binomial(n/d-1, d-1) * (-1)^(d-1) )}
%o A303506 for(n=1,100, print1(a(n),", "))
%Y A303506 Cf. A143862, A303340, A217668.
%K A303506 sign
%O A303506 1,8
%A A303506 _Paul D. Hanna_, Apr 25 2018