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A105639
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Multiples of coefficients in an asymptotic series of Ramanujan.
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0
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0, 1, 3, 51, 2635, 321315, 79244571, 35534634163, 26790753983211, 31980883597248195, 57639013468037578555, 150903079070698932214611, 555841597474333410204232203, 2804056152239296833617706906211, 18933384891214439885244043983467355
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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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FORMULA
| a(n)=-G(n)G(n+1) where G=A001469 Genocchi numbers.
Sum_{k>0} k^2/(e^(kx)-1) = zeta(3)2/x^3 -1/(12x) + Sum_{k>0} a(k)x^(2k-1)/((2k)!(2k+2)4(2^(2k)-1)(2^(2k+2)-1)).
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EXAMPLE
| x/1440 +x^3/181440 +x^5/7257600 +x^7/159667200 +691x^9/1569209241600 +...
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PROG
| (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
| Cf. A001469.
Sequence in context: A126685 A187666 A172434 * A003028 A069343 A084882
Adjacent sequences: A105636 A105637 A105638 * A105640 A105641 A105642
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 16 2005
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