OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..380
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 556
FORMULA
E.g.f.: 1/(1 - 2*x - 2*x^2).
a(n) = 2^n * A080599(n).
a(n) = 2*n*a(n+1) + 2*n*(n-1)*a(n), a(0) = 1, a(1) = 2.
a(n) = (n!/6) * Sum_{p = RootOf(2*z^2+2*z-1)} (1+2*p)*p^(-n-1).
a(n) = n!*A002605(n+1). - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Sequence(Union(Z, Z, Prod(Z, Union(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[1/(1-2x-2x^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 14 2015 *)
Table[n!*(-I*Sqrt[2])^(n)*ChebyshevU[n, I/Sqrt[2]], {n, 0, 40}] (* G. C. Greubel, Jan 31 2023 *)
PROG
(Magma) [n le 2 select n else 2*(n-1)*Self(n-1) + 2*(n-1)*(n-2)*Self(n-2): n in [1..41]]; // G. C. Greubel, Jan 31 2023
(SageMath)
A002605=BinaryRecurrenceSequence(2, 2, 0, 1)
[A052611(n) for n in range(41)] # G. C. Greubel, Jan 31 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved