A024293 Expansion of e.g.f. log(1 + sin(x)^2)/2 (even-indexed coefficients).

0, 1, -10, 256, -13840, 1282816, -181649920, 36478744576, -9861412096000, 3452931391553536, -1520176422094766080, 821908023102140317696, -535369559186849435484160, 413508899951810581475885056, -373681769282729298809313034240, 390605070751731814007608616943616

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

A(0,k) = 1 and A(n,k) = -(k*(k+1) * A(n-1,k+2) + k^2 * A(n-1,k)) for n > 0. a(0) = 0 and a(n) = A(n-1,2). - Seiichi Manyama, Apr 15 2026

Example

log(1 + sin(x)^2)/2 = x^2/2! - 10*x^4/4! + 256*x^6/6! - 13840*x^8/8! + 1282816*x^10/10! - ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Log[1+Sin[x]^2]/2, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, May 21 2014 *)

Crossrefs

Cf. A009344, A012494.

Sequence in context: A251588 A126468 A336665 * A361559 A120268 A001824

Adjacent sequences: A024290 A024291 A024292 * A024294 A024295 A024296

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs Mar 1997

Prior Mathematica program replaced by Harvey P. Dale, May 21 2014

Status

approved