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A096719 Numerators of terms in series expansion of arctan(arcsin(x)). 8
1, -1, 13, -173, 12409, -123379, 29518679, -889424791, 92273231203, 3836321172631, 22487012578592981, 2865860401219263691, 35970731592390474409, 277817773865257308429491, 1687365015862907602230599, 22415401434548677685890690591, 5789220720660809183499012532793, 2838956049184596030388390046497291 (list; graph; refs; listen; history; text; internal format)
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

Cf. A096720, A096718, A096664, A096671, A096712, A096716, A045688, A045689.

Sequence in context: A296585 A219021 A065544 * A296677 A295507 A109392

Adjacent sequences:  A096716 A096717 A096718 * A096720 A096721 A096722

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Aug 15 2004

STATUS

approved

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Last modified April 1 09:46 EDT 2020. Contains 333159 sequences. (Running on oeis4.)