A009103 - OEIS

A009103

Expansion of e.g.f. cos(x)/cos(log(1+x)).

1, 0, 0, -3, 11, -70, 534, -4725, 47753, -542988, 6859084, -95298995, 1444301715, -23711336922, 419190167434, -7939747234965, 160403009819921, -3442962495033400, 78246246638467512, -1877007578925506787

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OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

FORMULA

a(n) ~ n! * cos(1-exp(-Pi/2)) / ((exp(Pi/2)-1) * (exp(-Pi/2)-1)^n). - Vaclav Kotesovec, Jan 22 2015

MATHEMATICA

CoefficientList[Series[Cos[x]*Sec[Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(cos(x)/cos(log(1+x)))) \\ G. C. Greubel, Jul 26 2018

(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

CROSSREFS

Sequence in context: A018193 A121945 A009025 * A018192 A056665 A345030

Adjacent sequences: A009100 A009101 A009102 * A009104 A009105 A009106

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

STATUS

approved