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A129355
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G.f.: A(x) = Product_{n>=1} [ (1-x)^2*(1 + 2x + 3x^2 +...+ n*x^(n-1)) ].
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3
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1, -2, -2, 4, -1, 12, -26, 38, -51, 6, 98, -190, 138, 60, 132, -1296, 2990, -3738, 3350, -3752, 4077, 1194, -12272, 18528, -14848, 9018, -2002, 5644, -86729, 290596, -514158, 611070, -603150, 657792, -952808, 1406568, -1208636, -635286, 3507362, -5062866, 3791614
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OFFSET
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0,2
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COMMENTS
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a(k) == 1 (mod 2) at k = 4*A001318(n) for n>=0, where A001318 are the generalized pentagonal numbers: m(3m-1)/2, m=0,+-1,+-2,....
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LINKS
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FORMULA
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G.f.: A(x) = Product_{n>=1} ( 1 - (n+1)*x^n + n*x^(n+1) ) . G.f.: A(x) = Product_{n>=1} [ (1-x)*(1 + x + x^2 +...+ x^(n-1) - n*x^n) ] .
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EXAMPLE
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A(x) = (1 - 2x + x^2)(1 - 3x^2 + 2x^3)(1 - 4x^3 + 3x^4)(1 - 5x^4 + 4x^5)*...
Terms are even except at positions given by:
a(n) == 1 (mod 2) at n = [0, 4, 8, 20, 28, 48, 60, 88,...,4*A001318(n),...].
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PROG
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(PARI) a(n)=if(n==0, 1, polcoeff(prod(k=1, n, 1-(k+1)*x^k+k*x^(k+1)+x*O(x^n)), n))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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