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

0,3

Links

Table of n, a(n) for n=0..20.

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

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 *)

Prog

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

Crossrefs

Cf. A000023, A010842.

Sequence in context: A188325 A151028 A282619 * A318694 A281433 A277379

Adjacent sequences: A080249 A080250 A080251 * A080253 A080254 A080255

Keyword

easy,nonn

Author

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

Status

approved