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

0,3

Links

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

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.

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 *)

Prog

(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);

Crossrefs

Sequence in context: A004528 A066535 A134455 * A000643 A261489 A286936

Adjacent sequences: A191697 A191698 A191699 * A191701 A191702 A191703

Keyword

sign

Author

Vladimir Kruchinin, Jun 12 2011

Extensions

More terms from Harvey P. Dale, May 05 2013

Status

approved