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A145623
Numerator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.
2
68, 13126, 4200532, 1881839401, 361313167484, 254364469931206, 211631238983010892, 5417759717965164721, 2947261286573050252868, 17919348622364145592266214, 1146838311831305317954669876
OFFSET
1,1
COMMENTS
For denominators see A145624. For general properties of A_l(x) see A145609.
LINKS
FORMULA
Sum_{n >= 1} (a(n)/A145624(n))*x^n = (32*sqrt(x)*log((1+sqrt(x))/(1-sqrt(x))) - 4*log(1-x))/(1-64*x). - Robert Israel, Mar 09 2016
MAPLE
G:= (32*sqrt(x)*ln((1-sqrt(x))/(1+sqrt(x))) + 4*ln(1-x))/(64*x-1):
S:= series(G, x, 51):
seq(coeff(S, x, n), n=1..50); # Robert Israel, Mar 09 2016
MATHEMATICA
m = 8; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski, Oct 14 2008 *)
a[n_, m_]:=Integrate[(m-x^n)/(m-x), {x, 0, 1}]+(m^n-m)Log[m/(m-1)]
Table[8 a[2 n, 8] // Simplify // Numerator, {n, 1, 25}] (* Gerry Martens , Jun 04 2016 *)
CROSSREFS
Sequence in context: A331867 A267064 A159365 * A307137 A230685 A093234
KEYWORD
frac,nonn
AUTHOR
Artur Jasinski, Oct 14 2008
EXTENSIONS
Edited by R. J. Mathar, Aug 21 2009
STATUS
approved