The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A110708

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A110708

E.g.f. log(1+arctan(x)).
(history; published version)

#20 by N. J. A. Sloane at Sun Oct 29 21:47:00 EDT 2017

STATUS

proposed

approved

#19 by Tani Akinari at Sun Oct 29 18:40:26 EDT 2017

STATUS

editing

proposed

#18 by Tani Akinari at Sun Oct 29 18:38:36 EDT 2017

PROG

(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;

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 22 30 2017 */

STATUS

proposed

editing

#17 by Tani Akinari at Sun Oct 22 06:21:06 EDT 2017

STATUS

editing

proposed

#16 by Tani Akinari at Sun Oct 22 06:20:24 EDT 2017

PROG

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

STATUS

proposed

editing

#15 by Tani Akinari at Sun Oct 22 03:38:07 EDT 2017

STATUS

editing

proposed

Discussion

Sun Oct 22

04:00

Michel Marcus: can you move new Maxima prog after existing Maxima : see 5th bullet of https://oeis.org/wiki/Style_Sheet#Programs

#14 by Tani Akinari at Sun Oct 22 03:36:31 EDT 2017

PROG

(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 22 2017 */

STATUS

approved

editing

#13 by Alois P. Heinz at Wed Sep 06 20:39:30 EDT 2017

STATUS

proposed

approved

#12 by G. C. Greubel at Wed Sep 06 18:07:31 EDT 2017

STATUS

editing

proposed

#11 by G. C. Greubel at Wed Sep 06 18:07:22 EDT 2017

NAME

E.g.f. log(1+arctan(x)).

LINKS

G. C. Greubel, <a href="/A110708/b110708.txt">Table of n, a(n) for n = 0..450</a>

FORMULA

a(n) = n!*sum(Sum_{m=0..(n-1)/2, } (2^(2*m-n)*(n-2*m)!*(-1)^(n-m-1) *sum( Sum_{i=0..2*m, } (2^(i+n-2*m)*stirling1Stirling1(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

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

STATUS

approved

editing