A110708 E.g.f. log(1+arctan(x)).

0, 1, -1, 0, 2, 8, -64, -112, 2064, 8192, -157056, -599808, 16072704, 80010240, -2484268032, -13537247232, 506459129856, 3160676007936, -135526008225792, -929451393220608, 45507663438741504

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