A080252 a(n) = n*a(n-1)+4*a(n-2)-4*(n-2)*a(n-3).

0, 1, 2, 10, 40, 216, 1296, 9136, 73088, 658048, 6580480, 72386304, 868635648, 11292267520, 158091745280, 2371376195584, 37942019129344, 645014325264384, 11610257854758912, 220594899240681472, 4411897984813629440

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Feb 10 2003

Keywords

• easy
• nonn

Crossrefs

Cf. A000023, A010842.

Programs

Maple

A080252 := n -> (exp(2)*GAMMA(1+n,2) - exp(-2)*GAMMA(1+n,-2))/4:
seq(simplify(A080252(n)), n=0..20); # Peter Luschny, Dec 18 2017

Mathematica

c = CoefficientList[Series[(Sinh[z]*Cosh[z])/(1 - z), {z, 0, 25}], z]; For[n = 0, n < 25, n++; Print[c[[n]]*(n - 1)! ]]
RecurrenceTable[{a[0]==0,a[1]==1,a[2]==2,a[n]==n*a[n-1]+4a[n-2]-4(n-2)* a[n-3]}, a,{n,20}] (* Harvey P. Dale, Nov 17 2013 *)

PARI

x='x+O('x^99); concat([0], Vec(serlaplace(sinh(x)*cosh(x)/(1-x)))) \\ Altug Alkan, Dec 18 2017

Formula

E.g.f.: sinh(z)*cosh(z)/(1-z).

a(n) ~ n!*(e^2-1/e^2)/4. - Vaclav Kotesovec, Oct 13 2012

a(n) = (exp(2)*Gamma(1+n,2) - exp(-2)*Gamma(1+n,-2))/4 = (A010842(n) - A000023(n))/4. - Peter Luschny, Dec 18 2017