A195466 - OEIS

%I #26 Oct 11 2017 00:49:03

%S 45,945,14175,467775,638512875,1915538625,488462349375,7795859096025,

%T 32157918771103125,316985199315159375,3028793579456347828125,

%U 478230565177318078125,3952575621190533915703125,28304394023345413370350078125,7217620475953080409439269921875,21652861427859241228317809765625

%N Denominator of the coefficient of x^(2n) in expansion of 1/x^4 - 1/(3*x^2) - 1/(x^3*arctanh(x)).

%C Prepending 3 to the data gives the denominators of the odd powers in the expansion of 1/arctan(x). - _Peter Luschny_, Oct 04 2014

%F 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 + ...

%p A195466 := proc(n)

%p         1/x^4 -1/(3*x^2) -1/(x^3*arctanh(x)) ;

%p         coeftayl(%,x=0,2*n) ;

%p         denom(%) ;

%p end proc

%p seq(A195466(n),n=0..15) ;

%p # Or

%p seq(denom(coeff(series(1/arctan(x),x,2*n+2),x,2*n+1)),n=1..16); # _Peter Luschny_, Oct 04 2014

%t 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 *)

%Y Cf. A187870 (numerator).

%K nonn,frac

%O 0,1

%A _R. J. Mathar_, Sep 21 2011