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1, 0, 5, 6, 24, 40, 120, 250, 640, 1452, 3600, 8510, 20880, 50460, 124024, 303750, 750120, 1853120, 4600200, 11437548, 28527320, 71281800, 178526880, 447893250, 1125750120, 2833844040, 7144449920, 18036271740, 45591631800, 115381449692, 292329067800, 741410192250
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = (1/n) * Sum_{d|n} mu(n/d) * A001350(d)^2 = (1/n) * Sum_{d|n} mu(n/d) * A152152(d).
G.f.: Sum_{k>=1} mu(k) * log(f(x^k))/k , where f(x) = ((1-x-x^2) * (1+x-x^2))^2/((1-3*x+x^2) * (1-x)^2 * (1+x)^4). (End)
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PROG
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(PARI) a001350(n) = fibonacci(n+1)+fibonacci(n-1)-1-(-1)^n;
a(n) = sumdiv(n, d, moebius(n/d)*a001350(d)^2)/n; \\ Seiichi Manyama, Apr 29 2021
(PARI) f(x) = ((1-x-x^2)*(1+x-x^2))^2/((1-3*x+x^2)*(1-x)^2*(1+x)^4);
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*log(f(x^k))/k)) \\ Seiichi Manyama, Apr 29 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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