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A009132 Expansion of e.g.f. cosh(log(1+x))/exp(x). 2
1, -1, 2, -7, 31, -161, 976, -6847, 54797, -493201, 4932046, -54252551, 651030667, -8463398737, 118487582396, -1777313736031, 28437019776601, -483429336202337, 8701728051642202, -165332832981201991, 3306656659624039991 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = (-1)^n/2*floor(n!*exp(1)-n+1), n>0. - Vladeta Jovovic, Aug 17 2002

E.g.f.: (2+2*x+x^2)/(2*(1+x)*exp(x)) =(1+x/(G(0))/2 ; G(k) = 1 - 1/(1 + x + x^2 - (x*(1+x))^2/(x*(1+x) - (k+1)/(1 + x/G(k+1)))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 28 2011

MATHEMATICA

With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]]/Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 28 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/exp(x))) \\ G. C. Greubel, Jul 28 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Exp(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

CROSSREFS

Cf. A009578.

Sequence in context: A221958 A221957 A030966 * A125275 A007446 A277396

Adjacent sequences:  A009129 A009130 A009131 * A009133 A009134 A009135

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

STATUS

approved

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Last modified June 25 04:52 EDT 2021. Contains 345452 sequences. (Running on oeis4.)