login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110708 E.g.f. log(1+arctan(x)). 7
0, 1, -1, 0, 2, 8, -64, -112, 2064, 8192, -157056, -599808, 16072704, 80010240, -2484268032, -13537247232, 506459129856, 3160676007936, -135526008225792, -929451393220608, 45507663438741504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..450

FORMULA

a(n) = n!*Sum_{m=0..(n-1)/2} (2^(2*m-n)*(n-2*m)!*(-1)^(n-m-1) * Sum_{i=0..2*m} (2^(i+n-2*m)*Stirling1(n-2*m+i,n-2*m)*binomial(n-1,n-2*m+i-1))/(n-2*m+i)!))/(n-2*m).

MATHEMATICA

With[{nn = 50}, CoefficientList[Series[Log[1 + ArcTan[x]], {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Sep 06 2017 *)

PROG

(Maxima)

a(n):=2*n!*sum((2^(-(n-2*m)-1)*(n-2*m)!*(-1)^(n-m-1)*sum((2^(i+n-2*m)*stirling1(n-2*m+i, n-2*m)*binomial(n-1, n-2*m+i-1))/(n-2*m+i)!, i, 0, 2*m))/(n-2*m), m, 0, (n-1)/2);

(Maxima) b[1]:1$ b[n]:=sum((-1)^(k+1)*b[n-1-2*k]/(2*k+1), k, 0, floor(n/2)-1)+((%i)^(n-1)+(-%i)^(n-1))/2;

cons(0, makelist((n-1)!*b[n], n, 1, 100)); /* Tani Akinari, Oct 30 2017 */

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(log(1 + atan(x))))) \\ G. C. Greubel, Sep 06 2017

CROSSREFS

Sequence in context: A153526 A153554 A139018 * A295232 A287229 A323853

Adjacent sequences:  A110705 A110706 A110707 * A110709 A110710 A110711

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Jun 12 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)