The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052681 Expansion of e.g.f. (1-x)/(1 - x - x^2 - 2*x^3 + 2*x^4). 1
1, 0, 2, 18, 48, 840, 9360, 90720, 1653120, 25764480, 442713600, 9540115200, 201659673600, 4744989849600, 123531638630400, 3325415917824000, 97123590660096000, 3021564701675520000, 98526128957448192000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: (1-x)/(1 - x - x^2 - 2*x^3 + 2*x^4).
Recurrence: a(0)=1, a(1)=0, a(2)=2, a(3)=18, a(n+4) = (n+4)*a(n+3) + (12 + 7*n + n^2)*a(n+2) + (48 + 52*n + 18*n^2 + 2*n^3)*a(n+1) - 2*(n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*a(n).
a(n) = (n!/353)*Sum_{alpha=RootOf(1 - Z - z^2 - 2*Z^3 + 2*Z^4)} (18 + 106*alpha - 33*alpha^2 - 28*alpha^3)*alpha^(-1-n).
a(n) = n!*A052546(n). - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Sequence(Prod(Z, Z, Union(Z, Z, Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^2-2x^3+2x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 23 2014 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (1-x)/(1-x-x^2-2*x^3+2*x^4) ))); // G. C. Greubel, Jun 09 2022
(SageMath)
def A052681_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( (1-x)/(1-x-x^2-2*x^3+2*x^4) ).egf_to_ogf().list()
A052681_list(40) # G. C. Greubel, Jun 09 2022
CROSSREFS
Sequence in context: A304933 A126909 A139268 * A208652 A223469 A048910
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 14:10 EDT 2024. Contains 372952 sequences. (Running on oeis4.)