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A105639
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Multiples of coefficients in an asymptotic series of Ramanujan.
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1
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0, 1, 3, 51, 2635, 321315, 79244571, 35534634163, 26790753983211, 31980883597248195, 57639013468037578555, 150903079070698932214611, 555841597474333410204232203, 2804056152239296833617706906211, 18933384891214439885244043983467355
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OFFSET
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0,3
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REFERENCES
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G. H. Hardy, Srinivasa Ramanujan (1887-1920), pp. xxi-xxxvi of Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 2000. See page xxvi VII. (4)
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LINKS
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FORMULA
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a(n) = -G(n)G(n+1) where G=A001469 Genocchi numbers.
Sum_{k>0} k^2/(e^(k*x) - 1) = zeta(3)*2/x^3 - 1/(12*x) + Sum_{k>0} a(k)x^(2*k-1)/((2*k)!(2*k+2)*4*(2^(2*k)-1)*(2^(2*k+2)-1)).
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EXAMPLE
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x/1440 + x^3/181440 + x^5/7257600 + x^7/159667200 + 691x^9/1569209241600 + ...
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PROG
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(PARI) a(n)=if(n<0, 0, n*=2; -4*(2^n-1)*(4*2^n-1)*bernfrac(n)*bernfrac(n+2))
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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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