OFFSET
0,3
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
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Feb 10 2003
STATUS
approved