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Search: id:A105639
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| A105639 |
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Multiples of coefficients in an asymptotic series of Ramanujan. |
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+0
1
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| 0, 1, 3, 51, 2635, 321315, 79244571, 35534634163, 26790753983211, 31980883597248195, 57639013468037578555, 150903079070698932214611, 555841597474333410204232203, 2804056152239296833617706906211, 18933384891214439885244043983467355
(list; graph; listen)
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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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FORMULA
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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
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x/1440 +x^3/181440 +x^5/7257600 +x^7/159667200 +691x^9/1569209241600 +...
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PROGRAM
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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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Cf. A001469.
Sequence in context: A145242 A075869 A126685 this_sequence A003028 A069343 A084882
Adjacent sequences: A105636 A105637 A105638 this_sequence A105640 A105641 A105642
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Apr 16 2005
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