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%I #9 Nov 16 2017 13:16:35
%S 2,1,4,5,6,6,8,16,12,15,12,32,14,28,32,52,18,55,20,74,72,66,24,160,28,
%T 91,140,146,30,205,32,271,244,153,72,442,38,190,392,563,42,518,44,505,
%U 788,276,48,1510,52,451,852,896,54,1086,728,1748,1180,435,60,3291,62,496,1648,2867,1848,2101,68,2481,2072,1953,72,7634
%N G.f.: Sum_{n=-oo..+oo, n<>0} x^(n^2) / (1 - x^n)^(n+1).
%H Paul D. Hanna, <a href="/A261608/b261608.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Sum_{n=-oo..+oo, n<>0} x^n * (x^n - 1)^(n-1).
%F G.f.: Sum_{n=-oo..+oo} x^(n^2)/(1 + x^n)^n, where the sum is taken to exclude the coefficient of x^0.
%F G.f.: Sum_{n=-oo..+oo} (1 + x^n)^n, where the sum is taken to exclude the coefficient of x^0.
%F G.f.: x * d/dx Sum_{n=-oo..+oo, n<>0} (1/n^2) * x^(n^2)/(1 - x^n)^n. - _Paul D. Hanna_, Nov 16 2017
%e G.f.: A(x) = 2*x + x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 6*x^6 + 8*x^7 + 16*x^8 + 12*x^9 + 15*x^10 + 12*x^11 + 32*x^12 + 14*x^13 + 28*x^14 +...
%e where A(x) = N(x) + P(x) such that
%e N(x) = x*(x-1)^0 + x^2*(x^2-1) + x^3*(x^3-1)^2 + x^4*(x^4-1)^3 + x^5*(x^5-1)^4 + x^6*(x^6-1)^5 + x^7*(x^7-1)^6 + x^8*(x^8-1)^7 +...
%e P(x) = x/(1-x)^2 + x^4/(1-x^2)^3 + x^9/(1-x^3)^4 + x^16/(1-x^4)^5 + x^25/(1-x^5)^6 + x^36/(1-x^6)^7 + x^49/(1-x^7)^8 +...
%e explicitly,
%e N(x) = x - x^2 + x^3 + x^5 - 3*x^6 + x^7 + 2*x^8 + 2*x^9 - 5*x^10 + x^11 + x^12 + x^13 - 7*x^14 + 7*x^15 + 7*x^16 + x^17 - 19*x^18 + x^19 + 4*x^20 +...
%e P(x) = x + 2*x^2 + 3*x^3 + 5*x^4 + 5*x^5 + 9*x^6 + 7*x^7 + 14*x^8 + 10*x^9 + 20*x^10 + 11*x^11 + 31*x^12 + 13*x^13 + 35*x^14 + 25*x^15 +...
%o (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, if(m!=0, x^(m^2)/(1-x^m +x*O(x^n))^(m+1))), n)}
%o for(n=1, 60, print1(a(n), ", "))
%o (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, if(m!=0, x^m*(x^m-1 +x*O(x^n))^(m-1))), n)}
%o for(n=1, 60, print1(a(n), ", "))
%o (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, x^(m^2)/(1+x^m +x*O(x^n))^m), n)}
%o for(n=1, 60, print1(a(n), ", "))
%o (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, (1 + x^m +x*O(x^n))^m), n)}
%o for(n=1, 60, print1(a(n), ", "))
%Y Cf. A261605.
%K nonn
%O 1,1
%A _Paul D. Hanna_, Aug 26 2015
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