A088127 E.g.f. exp(-x)*cosh(x)/(1-x)^2.

1, 1, 4, 14, 72, 424, 2960, 23568, 211456, 2109056, 23150592, 277315840, 3599704064, 50331030528, 754122723328, 12054165272576, 204743835156480, 3682557441114112, 69920454322356224, 1397542619388248064, 29331932133035081728, 644973249444408197120

Offset: 0

Author

Paul Barry, Sep 19 2003

Keywords

• easy
• nonn

Comments

A088127(n)+A037256(n)=(n+1)! Binomial transform is A088128.

Links

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

Programs

Mathematica

Table[n!*SeriesCoefficient[E^(-x)*Cosh[x]/(1-x)^2,{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 14 2012 *)
With[{nn=30},CoefficientList[Series[Exp[-x] Cosh[x]/(1-x)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 24 2020 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(-x)*cosh(x)/(1-x)^2)) \\ Joerg Arndt, May 10 2013

Formula

Recurrence: a(n) = 2*(n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ n!*n*(1+1/e^2)/2. - Vaclav Kotesovec, Oct 14 2012