A080227 a(n) = n*a(n-1) + (1/2)*(1+(-1)^n), a(0)=0.

0, 0, 1, 3, 13, 65, 391, 2737, 21897, 197073, 1970731, 21678041, 260136493, 3381774409, 47344841727, 710172625905, 11362762014481, 193166954246177, 3477005176431187, 66063098352192553, 1321261967043851061, 27746501307920872281, 610423028774259190183

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Feb 07 2003

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A009179.

Programs

Mathematica

c=CoefficientList[Series[(e^x+e^(-x)-2)/(2(1-x)), {x, 0, 25}], x]; For[n = 0, n < 26, n++; Print[c[[n]]*(n - 1)! ]]
Join[{0},RecurrenceTable[{a[1]==0,a[2]==1,a[n]==(n-1)(a[n-1]+a[n-2])+ 1}, a[n],{n,30}]] (* Harvey P. Dale, Jul 21 2011 *)

Formula

E.g.f.: (exp(x) + exp(-x) - 2)/(2*(1 - x)).

a(n) = floor((cosh(1)-1)*n!). - Benoit Cloitre, Feb 14 2003

a(n) = (n-1)*(a(n-1) + a(n-2)) + 1 for n > 1. - Gary Detlefs, Jun 22 2010

a(n) = (1/2)*(exp(-1)*Gamma(n+1,-1) + exp(1)*Gamma(n+1,1)) - Gamma(n+1,0). - Martin Clever, Mar 26 2023