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A105639 Multiples of coefficients in an asymptotic series of Ramanujan. 1
0, 1, 3, 51, 2635, 321315, 79244571, 35534634163, 26790753983211, 31980883597248195, 57639013468037578555, 150903079070698932214611, 555841597474333410204232203, 2804056152239296833617706906211, 18933384891214439885244043983467355 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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)

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..158

FORMULA

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)).

EXAMPLE

x/1440 + x^3/181440 + x^5/7257600 + x^7/159667200 + 691x^9/1569209241600 + ...

PROG

(PARI) a(n)=if(n<0, 0, n*=2; -4*(2^n-1)*(4*2^n-1)*bernfrac(n)*bernfrac(n+2))

CROSSREFS

Cf. A001469.

Sequence in context: A187666 A172434 A210676 * A003028 A069343 A084882

Adjacent sequences:  A105636 A105637 A105638 * A105640 A105641 A105642

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 16 2005

STATUS

approved

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Last modified April 23 05:42 EDT 2021. Contains 343199 sequences. (Running on oeis4.)