A012079 cos(arcsin(tan(x)))=1-1/2!*x^2-11/4!*x^4-301/6!*x^6-16631/8!*x^8...

1, -1, -11, -301, -16631, -1620601, -250557251, -56629836901, -17602836565871, -7193368568377201, -3735581618747946491, -2401310609311293289501, -1871136400199563216523111

Offset

0,3

Links

Table of n, a(n) for n=0..12.

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

Bisection of A012253.

Sequence in context: A279181 A002114 A012192 * A180056 A172506 A250551

Adjacent sequences: A012076 A012077 A012078 * A012080 A012081 A012082

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved