OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..200
FORMULA
a(n) = b(2*n+1), b(n) = numerator(1/n*sum(m=1..n-1, (1-(-1)^(m))*(-1)^((m-1)/2)*(1+(-1)^(n-m))/4*sum(k=1..n-m, (sum(j=1..k, binomial(k,j)*2^(1-j)* sum(i=0..floor(j/2), (-1)^((n-m)/2-i-j)*binomial(j,i)*(j-2*i)^(n-m+j)/(n-m+j)!)))*binomial(k+n-1,n-1)))+(1-(-1)^(n))/(2)*(-1)^((n-1)/2)/n). - Vladimir Kruchinin, May 02 2011
EXAMPLE
arctan(arcsin(x)) = x - 1/6*x^3 + 13/120*x^5 - 173/5040*x^7 + 12409/362880*x^9 - 123379/13305600*x^11 + ...
MATHEMATICA
Numerator[Take[CoefficientList[Series[ArcTan[ArcSin[x]], {x, 0, 40}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 18 2016 *)
PROG
(Maxima)
a(n):=b(2*n+1);
b(n):=num(1/n*sum((1-(-1)^(m))*(-1)^((m-1)/2)*(1+(-1)^(n-m))/4*sum((sum(binomial(k, j)*2^(1-j)*sum((-1)^((n-m)/2-i-j)*binomial(j, i)*(j-2*i)^(n-m+j)/(n-m+j)!, i, 0, floor(j/2)), j, 1, k))*binomial(k+n-1, n-1), k, 1, n-m), m, 1, n-1)+(1-(-1)^(n))/(2)*(-1)^((n-1)/2)/n); /* Vladimir Kruchinin, May 02 2011 */
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Aug 15 2004
STATUS
approved