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A185653 Expansion of exp( Sum_{n>=1} -3*sigma(2n)*x^n/n ) in powers of x. 2

%I #10 Jun 12 2015 23:07:38

%S 1,-9,30,-39,0,18,49,0,-192,110,81,78,-130,0,-30,-121,0,210,320,-270,

%T 0,-407,0,192,190,0,0,0,351,-210,-418,0,-510,448,0,462,611,0,-960,50,

%U 0,0,-350,0,450,-361,-162,960,0,0,798,-782,0,-1170,-290,-441,702,850,0,0,576

%N Expansion of exp( Sum_{n>=1} -3*sigma(2n)*x^n/n ) in powers of x.

%C When is a(n) zero (A258867)?

%H Paul D. Hanna, <a href="/A185653/b185653.txt">Table of n, a(n) for n = 0..1024</a>

%F Expansion of q^(-1/8)*eta(q)^9/eta(q^2)^3 in powers of q; equals the self-convolution cube of A115110 [See formula of Michael Somos for A115110].

%e G.f. = 1 - 9*x + 30*x^2 - 39*x^3 + 18*x^5 + 49*x^6 - 192*x^8 + 110*x^9 + ...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,-3*sigma(2*m)*x^m/m)+x*O(x^n)),n)}

%o (PARI) {a(n)=local(X=x+x*O(x^n));polcoeff(eta(X)^9/eta(X^2)^3,n)}

%Y Cf. A115110, A000203, A258867.

%K sign

%O 0,2

%A _Paul D. Hanna_, Feb 16 2011

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