A191700 E.g.f. 1/(1-arctan(x)).

1, 1, 2, 4, 8, 24, 128, 624, 1920, 8448, 137472, 1203456, 835584, -23073792, 1024616448, 15237156864, -88263327744, -2230875095040, 37715465207808, 842231374479360, -10018210447097856, -278334129792614400, 4502327717477744640, 131853718231347363840

Offset: 0

Author

Vladimir Kruchinin, Jun 12 2011

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Programs

Mathematica

With[{nn=30},CoefficientList[Series[1/(1-ArcTan[x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 05 2013 *)
Flatten[{1, Table[n!*Sum[k!*(-1)^((3*n+k)/2)*Sum[2^i*StirlingS1[i, k]*Binomial[n-1, i-1]/i!, {i, k, n}]/2^k, {k, 1, n}], {n, 1, 25}]}] (* Vaclav Kotesovec, Sep 23 2016 *)

Maxima

a(n):=n!*sum((k!*(-1)^((3*n+k)/2)*sum((2^i*stirling1(i,k)*binomial(n-1,i-1))/i!,i,k,n))/2^k,k,1,n);

Formula

a(n)=n!*sum(k=1..n, (k!*(-1)^((3*n+k)/2)*sum(i=k..n,(2^i*stirling1(i,k)*binomial(n-1,i-1))/i!))/2^k),n>0, a(0)=1.

Extensions

More terms from Harvey P. Dale, May 05 2013