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A013331 Expansion of e.g.f. arctan(exp(x) - sec(x)). 1
0, 1, 0, -1, -4, 5, 60, -61, -2504, -8695, 100920, 873479, -6889804, -142058995, -4843020, 19728547019, 98903242096, -3531831462895, -49401992303760, 493517141932559, 17048746833049196, -29344831492412395, -6329111550017193300, -46994369824929657901, 2170046335781374467496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

EXAMPLE

x - 1/3!*x^3 - 4/4!*x^4 + 5/5!*x^5 + 60/6!*x^6 ...

MATHEMATICA

Range[0, 30]! CoefficientList[Series[ArcTan[Exp[x] - Sec[x]], {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2018 *)

PROG

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Arctan(Exp(x) - Sec(x)))); [0] cat [Factorial(n-1)*b[n]: n in [2..m]]; // Vincenzo Librandi, Aug 06 2018

(PARI) x = 'x + O('x^30); concat(0, Vec(serlaplace(atan(exp(x) - 1/cos(x))))) \\ Michel Marcus, Aug 06 2018

CROSSREFS

Sequence in context: A041941 A220534 A341575 * A226145 A042425 A109348

Adjacent sequences:  A013328 A013329 A013330 * A013332 A013333 A013334

KEYWORD

sign

AUTHOR

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

EXTENSIONS

a(0)=0 inserted and title improved by Sean A. Irvine, Aug 05 2018

STATUS

approved

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Last modified October 17 16:34 EDT 2021. Contains 348065 sequences. (Running on oeis4.)