OFFSET
0,3
FORMULA
a(n)=-(2*sum(k=1..2*n, (C(k-1)*sum(j=2*k..2*n, binomial(j-1,2*k-1)*j!*2^(2*n-j-2*k)*(-1)^((n+k)+j)*stirling2(2*n,j))))) with n>0, a(0)=1, C(n)=A000108(n) (Catalan numbers). [Vladimir Kruchinin, Oct 08 2012]
MATHEMATICA
With[{nn=30}, Take[CoefficientList[Series[Cos[ArcSin[Tan[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jan 23 2019 *)
PROG
(Maxima) a[n]:=if n=0 then 1 else -2*sum(binomial(2*k-2, k-1)/k*sum(binomial(j-1, 2*k-1)*j!*2^(2*n-j+(-2)*k)*(-1)^(n+k+j)*stirling2(2*n, j), j, 2*k, 2*n), k, 1, 2*n); makelist(a[n], n, 0, 12); [Vladimir Kruchinin, Oct 08 2012]
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved