The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A052674 Expansion of e.g.f. (1-x)/(1-3*x-2*x^2+2*x^3). 1
 1, 2, 16, 156, 2160, 36720, 753120, 17992800, 491500800, 15102339840, 515630707200, 19365156518400, 793401964185600, 35214960849868800, 1683239666985676800, 86204093846846976000, 4709107007890661376000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..350 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 622 FORMULA E.g.f.: (1 - x)/((1 + x)*(1 - 4*x + 2*x^2)). Recurrence: a(0)=1, a(1)=2, a(2)=16, a(n) = 3*n*a(n-1) + 2*n*(n-1)*a(n-2) - 2*n*(n-1)*(n-2)*a(n-3). a(n) = (n!/98)*Sum_{alpha=RootOf(1 -3*Z -2*Z^2 +2*Z^3)} (13 + 25*alpha - 16*alpha^2)*alpha^(-1-n). a(n) = n!*A052543(n). - R. J. Mathar, Nov 27 2011 a(n) = (n!/7)*(2*(-1)^n + 2^(n/2)*( 5*ChebyshevU(n, sqrt(2)) - 2*sqrt(2)*ChebyshevU(n-1, sqrt(2)) ). - G. C. Greubel, Jun 12 2022 MAPLE spec := [S, {S=Sequence(Prod(Union(Z, Z), Union(Z, Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA Table[(n!/7)*(2*(-1)^n + 2^(n/2)*(5*ChebyshevU[n, Sqrt[2]] - 2*Sqrt[2]*ChebyshevU[n - 1, Sqrt[2]])), {n, 0, 30}] (* G. C. Greubel, Jun 12 2022 *) PROG (Magma) R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1-x)/((1+x)*(1-4*x+2*x^2)) ))); // G. C. Greubel, Jun 12 2022 (SageMath) [factorial(n)*(2^(n/2)*(5*chebyshev_U(n, sqrt(2)) - 2*sqrt(2)*chebyshev_U(n-1, sqrt(2))) + 2*(-1)^n)/7 for n in (0..30)] # G. C. Greubel, Jun 12 2022 CROSSREFS Cf. A000142, A052543. Sequence in context: A012391 A012387 A009518 * A259706 A309440 A226012 Adjacent sequences:  A052671 A052672 A052673 * A052675 A052676 A052677 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 15 02:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)