A013101 Expansion of sec(arcsinh(x) + tan(x)) (coefficients of even powers only).

1, 4, 88, 5014, 527624, 89331514, 22153827556, 7576868616438, 3416549387012336, 1964348168375260594, 1402481265951220466076, 1217416473808119071396046, 1262628491065344385303595816

Offset

0,2

Links

Iain Fox, Table of n, a(n) for n = 0..213

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A281180 A296465 A012946 * A013067 A012996 A195373

Adjacent sequences: A013098 A013099 A013100 * A013102 A013103 A013104

Keyword

nonn

Author

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

Status

approved