A024264 - OEIS

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A024264

Expansion of tan(sin(x)^2)/2.

0, 1, -4, 136, -6784, 524416, -64036864, 10501374976, -2283962220544, 634741960278016, -218778649767706624, 91736006502034702336, -45959204407743090786304, 27112425203442398670094336, -18603328214677391682184413184, 14689562944237012958430694998016

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

FORMULA

a(n) = (2*n)! * [x^(2*n)] tan(sin(x)^2)/2.

a(n) ~ (2*n)! * (-1)^(n+1) / (sqrt(Pi*(2+Pi)) * (log(sqrt(Pi/2) + sqrt(1 + Pi/2)))^(2*n+1)). - Vaclav Kotesovec, Feb 04 2015

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Tan[Sin[x]^2]/2, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jan 30 2013 *)

CROSSREFS

Cf. A009675.