A156177 A bisection of A000436.

1, 352, 7869952, 1243925143552, 722906928498737152, 1118389087843083461066752, 3794717805092151129643367268352, 24809622030942586708931326728787197952, 284876472796397041595189052788763077537431552, 5358281136280777382502986500754127200892786313265152

Offset: 0

Author

N. J. A. Sloane, Nov 07 2009

Keywords

• nonn

Programs

Maple

a := n -> 2^(8*n+1)*3^(4*n)*(Zeta(0,-4*n,1/6)-Zeta(0,-4*n,2/3)):
seq(a(n), n=0..9); # Peter Luschny, Mar 11 2015

Mathematica

b[0] = 1; b[n_] := b[n] = (-1)^n (1-Sum[(-1)^i Binomial[2n, 2i] 3^(2n-2i) b[i], {i, 0, n-1}]);
a[n_] := b[2n];
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Jul 08 2019 *)

Sage

from mpmath import mp, lerchphi
mp.dps = 64; mp.pretty = True
def A156177(n): return abs(3^(4*n)*2^(4*n+1)*lerchphi(-1,-4*n,1/3))
[int(A156177(n)) for n in (0..9)]  # Peter Luschny, Apr 27 2013

Formula

a(n) = | 3^(4*n)*2^(4*n+1)*lerchphi(-1,-4*n,1/3) |. - Peter Luschny, Apr 27 2013

a(n) = 2^(8*n+1)*3^(4*n)*(zeta(-4*n,1/6)-zeta(-4*n,2/3)), where zeta(a,z) is the generalized Riemann zeta function. - Peter Luschny, Mar 11 2015