A024236 Expansion of log(1+tan(x)*x)/2.
0, 1, -2, 48, -1040, 62720, -4314624, 498003968, -70081316864, 13529482592256, -3175495421788160, 933402531586899968, -326784893253162369024, 136568449424117316190208, -66517446960602151366164480
Offset: 0
Keywords
Programs
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Maple
S:= series(log(1+tan(x)*x)/2, x, 101): seq(coeff(S, x, 2*j)*(2*j)!, j=0..50); # Robert Israel, Jun 29 2015
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Mathematica
With[{nn=30},Take[CoefficientList[Series[Log[1+Tan[x]x]/2,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Jun 24 2018 *)
Formula
E.g.f. of aerated sequence: Sum(n>=0, a(n)*x^(2*n)/(2*n)!) = log(1+tan(x)*x)/2. - Robert Israel, Jun 29 2015
Extensions
Extended with signs, Mar 1997
Previous Mathematica program replaced by Harvey P. Dale, Jun 24 2018