A131137 -id:A131137 - cp's OEIS frontend

A131138 a(n)=log_3(A131137(n)).

0, 1, 2, 3, 3, 4, 5, 5, 6, 7, 6, 7, 8, 8, 9, 10, 10, 11, 12, 11, 12, 13, 13, 14, 15, 15, 16, 17, 15, 16, 17, 17, 18, 19, 19, 20, 21, 20, 21, 22, 22, 23, 24, 24, 25, 26, 25, 26, 27, 27, 28, 29, 29, 30, 31, 29, 30, 31, 31, 32, 33, 33, 34, 35, 34, 35, 36, 36

Offset: 0

Paul Barry, Jun 17 2007

a(n)=if(n<4,n,valuation(denominator(polylog(1-n,1/4)/4),3)) \\ Charles R Greathouse IV, Jul 15 2014

A210244 Numerators of the polylogarithm li(-n,-1/2)/2.

Original entry on oeis.org

-1, -1, 1, 5, -7, -49, -53, 2215, 1259, -14201, -183197, 248885, 9583753, 14525053, -554173253, -4573299625, 99833187251, 215440236599, -1654012631597, -84480933600305, -36267273557287, 10992430255511053, 117548575473066241, -1380910044674479865

Offset: 1

Stanislav Sykora, Mar 19 2012

Given an integer n>0, consider the infinite series s(n) = li(-n,-1/2) = Sum_{k>=1} (-1)^k*k^n/2^k. Then s(n)=2*a(n)/A131137(n+1).

			s(1)=-2/9, s(2)=-2/27, s(3)=+2/27, s(4)=+10/81.

S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), Stan's Library Vol.I, April 2006, updated March 2012. See Eq.(29).
Eric W. Weisstein, MathWorld: Polylogarithm

Denominators: A131137, offset by 1.

Cf. A212846.

nn = 30; s[0] = 1; Do[s[n+1] = (-1/3) Sum[Binomial[n+1,i] s[i], {i, 0, n}], {n, 0, nn}]; Numerator[Table[s[n], {n, 0, nn}]] (* T. D. Noe, Mar 20 2012 *)
Table[PolyLog[-n, -1/2]/2, {n, 30}] (* T. D. Noe, Mar 23 2012 *)

a(n)=numerator(polylog(-n,-1/2)/2) \\ Charles R Greathouse IV, Jul 15 2014

Recurrence: s(n+1)=(-1/3)*Sum_{i=0..n} binomial(n+1,i)*s(i), with the starting value of s(0)=2/3.

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A131138 a(n)=log_3(A131137(n)).

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A210244 Numerators of the polylogarithm li(-n,-1/2)/2.

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