|
|
A145621
|
|
Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=7.
|
|
2
|
|
|
105, 31087, 2538991, 248821433, 21946050833, 11828921402977, 7535022933740305, 3692161237533130831, 1025190103621701235981, 954451986471803883166747, 15589382445706130101521201
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
For denominators see A145622. For general properties of A_l(x) see A145609.
|
|
LINKS
|
|
|
MAPLE
|
f:= n -> numer(add(7^(2*n+1-d)/d, d=1..2*n)):
|
|
MATHEMATICA
|
m = 7; 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 *)
a[n_, m_]:=Integrate[(m-x^n)/(m-x), {x, 0, 1}]+(m^n-m)Log[m/(m-1)]
Table[7 a[2 n, 7] // FullSimplify // Numerator, {n, 1, 25}] (* Gerry Martens , Jun 04 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|