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1, 352, 7869952, 1243925143552, 722906928498737152, 1118389087843083461066752, 3794717805092151129643367268352, 24809622030942586708931326728787197952, 284876472796397041595189052788763077537431552, 5358281136280777382502986500754127200892786313265152
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MAPLE
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a := n -> 2^(8*n+1)*3^(4*n)*(Zeta(0, -4*n, 1/6)-Zeta(0, -4*n, 2/3)):
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MATHEMATICA
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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];
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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