A273352 a(n) = 2^(2n+2) F(n) where F(n) is Ramanujan's F(n) = Sum_{k>=1} k^(4n-1)/(e^(Pi*k)-1) - 16^n* Sum_{k>=1} k^(4n-1)/(e^(4*Pi*k)-1).

1, 34, 11056, 14873104, 56814228736, 495812444583424, 8575634961418940416, 265929039218907754399744, 13722623393637762299131396096, 1112372064432735526930220874072064, 135292015985218004848567636630910795776, 23782283324940089109797537284278352042000384

Offset: 1

Author

Marko Riedel, May 20 2016

Keywords

• nonn

Comments

Bisection of the reduced tangent numbers, A002105. This follows from the formulas. - Franklin T. Adams-Watters, May 22 2016

Links

• Math.Stackexchange.Com, Marko R. Riedel et al., Closed form of a sum by Ramanujan

Crossrefs

Cf. A002105.

Cf. A000182 (m=2), A293951 (m=3), this seq (m=4), A318258 (m=5).

Programs

Maple

S := proc(n, k) option remember;
if k=0 then `if`(n=0, 1, 0) else S(n, k-1) + S(n-1, n-k) fi end:
A273352 := n -> S(4*n-1, 4*n-1)/2^(2*n-1):
seq(A273352(n), n=1..12); # Peter Luschny, Jan 18 2017

Mathematica

Table[2^(2*n + 2)*BernoulliB[4*n]*(1 - 2^(4*n))/(8*n), {n, 1, 10}] (* G. C. Greubel, May 21 2016 *)
(* Function LMLlist defined in A293951 *)
LMLlist[4, 13] (* Peter Luschny, Aug 26 2018 *)

Formula

a(n) = 2^{2*n+2} * Bernoulli(4*n) * (1-2^(4*n))/(8*n).