|
|
A195466
|
|
Denominator of the coefficient of x^(2n) in expansion of 1/x^4 - 1/(3*x^2) - 1/(x^3*arctanh(x)).
|
|
3
|
|
|
45, 945, 14175, 467775, 638512875, 1915538625, 488462349375, 7795859096025, 32157918771103125, 316985199315159375, 3028793579456347828125, 478230565177318078125, 3952575621190533915703125, 28304394023345413370350078125, 7217620475953080409439269921875, 21652861427859241228317809765625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Prepending 3 to the data gives the denominators of the odd powers in the expansion of 1/arctan(x). - Peter Luschny, Oct 04 2014
|
|
LINKS
|
|
|
FORMULA
|
1/x^4 - 1/(3x^2) - 1/(x^3*arctanh x) = 4/45 + 44*x^2/945 + 428*x^4/14175 + 10196*x^6/467775 + ...
|
|
MAPLE
|
1/x^4 -1/(3*x^2) -1/(x^3*arctanh(x)) ;
coeftayl(%, x=0, 2*n) ;
denom(%) ;
end proc
# Or
seq(denom(coeff(series(1/arctan(x), x, 2*n+2), x, 2*n+1)), n=1..16); # Peter Luschny, Oct 04 2014
|
|
MATHEMATICA
|
a[n_] := Sum[(2^(j+1)*Binomial[2*n+3, j]*Sum[(k!*StirlingS1[j+k, j]*StirlingS2[j+1, k])/(j+k)!, {k, 0, j+1}])/(j+1), {j, 0, 2*n+3}]/(2*n+3); Table[a[n] // Denominator, {n, 0, 15}] (* Jean-François Alcover, Jul 03 2013, after Vladimir Kruchinin's formula in A216272 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|