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A203860 G.f.: Product_{n>=1} (1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) where Lucas(n) = A000204(n).

%I A203860 #16 Mar 30 2012 18:37:34
%S A203860 1,-1,-4,-1,1,11,7,25,18,-11,-1,0,-325,-199,122,-1364,-843,550,0,11,
%T A203860 123,0,39650,24476,-15126,0,271443,164194,-103682,-1364,-1,-24476,0,
%U A203860 -9349,-123,-20633239,-12752043,7881225,-843,0,-226965629,-141422125,88114450,0,1
%N A203860 G.f.: Product_{n>=1} (1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) where Lucas(n) = A000204(n).
%C A203860 a(A093519(n)) = 0 where A093519 lists numbers that are not equal to the sum of two generalized pentagonal numbers.
%H A203860 Paul D. Hanna, <a href="/A203860/b203860.txt">Table of n, a(n) for n = 0..1000</a>
%F A203860 G.f.: exp( Sum_{n>=1} -sigma(n) * A000204(n) * x^n/n ).
%e A203860 G.f.: A(x) = 1 - x - 4*x^2 - x^3 + x^4 + 11*x^5 + 7*x^6 + 25*x^7 +...
%e A203860 -log(A(x)) = x + 3*3*x^2/2 + 4*4*x^3/3 + 7*7*x^4/4 + 6*11*x^5/5 + 12*18*x^6/6 +...+ sigma(n)*A000204(n)*x^n/n +...
%e A203860 The g.f. equals the product:
%e A203860 A(x) = (1-x-x^2) * (1-3*x^2+x^4) * (1-4*x^3-x^6) * (1-7*x^4+x^8) * (1-11*x^5-x^10) * (1-18*x^6+x^12) *...* (1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) *...
%e A203860 Positions of zeros form A093519:
%e A203860 [11,18,21,25,32,39,43,46,49,54,60,65,67,68,74,76,81,87,88,90,...]
%e A203860 which are numbers that are not the sum of two generalized pentagonal numbers.
%o A203860 (PARI) /* Subroutine used in PARI programs below: */
%o A203860 {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
%o A203860 (PARI) {a(n)=polcoeff(exp(sum(k=1, n, -sigma(k)*Lucas(k)*x^k/k)+x*O(x^n)), n)}
%o A203860 (PARI) {a(n)=polcoeff(prod(m=1, n, 1 - Lucas(m)*x^m + (-1)^m*x^(2*m) +x*O(x^n)), n)}
%Y A203860 Cf. A203861, A203850, A156234, A093519.
%K A203860 sign
%O A203860 0,3
%A A203860 _Paul D. Hanna_, Jan 07 2012