OFFSET
0,3
FORMULA
a(n) = (2*n)!*sum(k=1..2*n, ((2*k)!*binomial(2*k-2,k-1)*(-1)^(n+k+1)*sum(i=2*k..2*n, (2^(i+1)*stirling1(i,2*k)*binomial(2*n-1,i-1))/i!))/(k*2^(4*k))) with n>0, a(0)=1. [Vladimir Kruchinin, Oct 08 2012]
MATHEMATICA
With[{nn=30}, Take[CoefficientList[Series[Cos[ArcSin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Feb 07 2015 *)
PROG
(Maxima) a[n]:=if n=0 then 1 else (2*n)!*sum(((2*k)!*binomial(2*k-2, k-1)*(-1)^(n+k+1)*sum((2^(i+1)*stirling1(i, 2*k)*binomial(2*n-1, i-1))/i!, i, 2*k, 2*n))/(k*2^(4*k)), k, 1, 2*n); makelist(a[n], n, 0, 13); /* Vladimir Kruchinin, Oct 08 2012 */
CROSSREFS
KEYWORD
sign,changed
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved