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A209445
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a(n) = Pell(n)*A001227(n) for n >= 1, where A001227(n) is the number of odd divisors of n.
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3
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1, 2, 10, 12, 58, 140, 338, 408, 2955, 4756, 11482, 27720, 66922, 161564, 780100, 470832, 2273378, 8232630, 13250218, 31988856, 154455860, 186444716, 450117362, 1086679440, 3935214363, 6333631924, 30581480180, 36915112104, 89120964298, 430314081400, 519435045698
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OFFSET
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1,2
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COMMENTS
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Compare g.f. to the Lambert series of A001227: Sum_{n>=1} x^(2*n-1)/(1 - x^(2*n-1)).
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LINKS
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FORMULA
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G.f.: Sum_{n>=1} Pell(2*n-1)*x^(2*n-1)/(1 - A002203(2*n-1)*x^(2*n-1)-x^(4*n-2)), where A002203(n) = Pell(n-1) + Pell(n+1).
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EXAMPLE
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G.f.: A(x) = x + 2*x^2 + 10*x^3 + 12*x^4 + 58*x^5 + 140*x^6 + 338*x^7 + ...
where A(x) = 1*1*x + 2*1*x^2 + 5*2*x^3 + 12*1*x^4 + 29*2*x^5 + 70*2*x^6 + 169*2*x^7 + 408*1*x^8 + ... + Pell(n)*A001227(n)*x^n + ...
The g.f. is also given by the identity:
A(x) = 1*x/(1-2*x-x^2) + 5*x^3/(1-14*x^3-x^6) + 29*x^5/(1-82*x^5-x^10) + 169*x^7/(1-478*x^7-x^14) + 985*x^9/(1-2786*x^9-x^18) + 5741*x^11/(1-16238*x^11-x^22) + ...
which involves odd-indexed Pell and A002203 numbers.
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MATHEMATICA
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PROG
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(PARI) {Pell(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)), n)}
{a(n)=polcoeff(sum(m=1, n, Pell(2*m-1)*x^(2*m-1)/(1-A002203(2*m-1)*x^(2*m-1)-x^(4*m-2)+x*O(x^n))), n)}
for(n=1, 40, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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