A010789 Expansion of -arcsin(log(cos(x))) = (1/2!)*x^2 + (2/4!)*x^4 + (31/6!)*x^6 + (692/8!)*x^8 + ...

0, 1, 2, 31, 692, 32821, 2182982, 220761451, 29587628072, 5271224958121, 1181874030353162, 329170919623534231, 110868894348113861852, 44548277847630426340381, 21016319125189602127144142, 11511508896932068502821046371, 7241614305987283988489059076432

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = -1 * (2n)! [x^(2n)] arcsin(log(cos(x))). - Alois P. Heinz, Jun 11 2018

Mathematica

With[{nn=40}, Take[-CoefficientList[Series[ArcSin[Log[Cos[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 04 2025 *)

Crossrefs

Sequence in context: A058244 A245051 A024235 * A333349 A349071 A224863

Adjacent sequences: A010786 A010787 A010788 * A010790 A010791 A010792

Keyword

nonn

Author

Patrick Demichel

Extensions

a(0) = 0 prepended by Sean A. Irvine, Jun 11 2018

Status

approved