A012379 Expansion of e.g.f. cos(tan(x)*arcsin(x)) (even powers only).

1, 0, -12, -360, -14000, -705600, -42520896, -2581394816, -50539790080, 43910434596864, 18893865109070848, 6357906196273494016, 1895076999147133456384, 366371561754009899909120, -176926962056569654501195776, -397908136700956338408562851840, -528899949644745117870350321778688

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..225

Example

1 - (12/4!)*x^4 - (360/6!)*x^6 - (14000/8!)*x^8 - ...

Maple

S:= series(cos(tan(x)*arcsin(x)), x, 51):
seq(coeff(S, x, 2*j)*(2*j)!, j=0..25); # Robert Israel, Jan 06 2019

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Cos[Tan[x]ArcSin[x]], {x, 0, nn}], x]Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jan 26 2012 *)

Prog

(Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!Cos(Tan(x)*Arcsin(x))); [Factorial(n-1)*b[n]: n in [1..m-1 by 2]]; // Vincenzo Librandi, Jan 07 2019

Crossrefs

Sequence in context: A130213 A012633 A009079 * A012424 A009165 A012627

Adjacent sequences: A012376 A012377 A012378 * A012380 A012381 A012382

Keyword

sign

Author

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

Extensions

More terms from Robert Israel, Jan 06 2019

Status

approved