login
A bisection of A000436.
2

%I #16 Mar 19 2020 16:35:20

%S 1,352,7869952,1243925143552,722906928498737152,

%T 1118389087843083461066752,3794717805092151129643367268352,

%U 24809622030942586708931326728787197952,284876472796397041595189052788763077537431552,5358281136280777382502986500754127200892786313265152

%N A bisection of A000436.

%F a(n) = | 3^(4*n)*2^(4*n+1)*lerchphi(-1,-4*n,1/3) |. - _Peter Luschny_, Apr 27 2013

%F 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

%p a := n -> 2^(8*n+1)*3^(4*n)*(Zeta(0,-4*n,1/6)-Zeta(0,-4*n,2/3)):

%p seq(a(n), n=0..9); # _Peter Luschny_, Mar 11 2015

%t 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}]);

%t a[n_] := b[2n];

%t Table[a[n], {n, 0, 9}] (* _Jean-François Alcover_, Jul 08 2019 *)

%o (Sage)

%o from mpmath import mp, lerchphi

%o mp.dps = 64; mp.pretty = True

%o def A156177(n): return abs(3^(4*n)*2^(4*n+1)*lerchphi(-1,-4*n,1/3))

%o [int(A156177(n)) for n in (0..9)] # _Peter Luschny_, Apr 27 2013

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 07 2009