A013101 - OEIS

%I #15 Nov 28 2017 11:48:56

%S 1,4,88,5014,527624,89331514,22153827556,7576868616438,

%T 3416549387012336,1964348168375260594,1402481265951220466076,

%U 1217416473808119071396046,1262628491065344385303595816

%N Expansion of sec(arcsinh(x) + tan(x)) (coefficients of even powers only).

%H Iain Fox, <a href="/A013101/b013101.txt">Table of n, a(n) for n = 0..213</a>

%e 1 + (4/2!)*x^2 + (88/4!)*x^4 + (5014/6!)*x^6 + (527624/8!)*x^8 + ...

%t With[{nn=30},Take[CoefficientList[Series[Sec[ArcSinh[x]+Tan[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Nov 24 2017 *)

%o (PARI) first(n) = { x='x+O('x^(2*n-2)); vecextract(Vec(serlaplace(1/cos(asinh(x)+tan(x)))), sum(i=0, n-1, 2^(2*i))); } \\ _Iain Fox_, Nov 26 2017

%K nonn

%O 0,2

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