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A166879
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G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)/2*x^n/n ).
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3
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1, 1, 9, 473, 166969, 371186249, 5020831641761, 407273265807001089, 196573413317730320842177, 561769503571822735164882969633, 9474113076734769687535254457293566857, 940665572280219007549184269220597591870817337
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OFFSET
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0,3
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COMMENTS
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A002203 equals the logarithmic derivative of the Pell numbers (A000129).
Note that A002203(n^2) = (1+sqrt(2))^(n^2) + (1-sqrt(2))^(n^2).
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LINKS
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FORMULA
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a(n) == 1 (mod 8).
a(n) = (1/n)*Sum_{k=1..n} A002203(k^2)/2*a(n-k) for n>0 with a(0)=1.
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EXAMPLE
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G.f.: A(x) = 1 + x + 9*x^2 + 473*x^3 + 166969*x^4 + 371186249*x^5 +...
log(A(x)) = x + 17*x^2/2 + 1393*x^3/3 + 665857*x^4/4 + 1855077841*x^5/5 + 30122754096401*x^6/6 + 2850877693509864481*x^7/7 +...+ A002203(n^2)/2*x^n/n +...
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PROG
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(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(m=1, n, polcoeff((1-x)/(1-2*x-x^2+x*O(x^(m^2))), m^2)*x^m/m)+x*O(x^n)), n))}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, polcoeff((1-x)/(1-2*x-x^2+x*O(x^(k^2))), k^2)*a(n-k)))}
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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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