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 A052556 Expansion of e.g.f. 1/(1-x-x^3). 1
 1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400, 1636588800, 28740096000, 547977830400, 11245999564800, 247150455552000, 5795612798976000, 144409095806976000, 3809412354908160000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..420 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 497 FORMULA E.g.f.: 1/(1-x-x^3). a(n) = n*a(n-1) + n*(n-1)*(n-2)*a(n-3), with a(0)=1, a(1)=1, a(2)=2. a(n) = Sum(1/31*(4+6*_alpha^2+9*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!. a(n) = n! * A000930(n). - R. J. Mathar, Nov 27 2011 MAPLE spec := [S, {S=Sequence(Union(Z, Prod(Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA With[{nn=30}, CoefficientList[Series[1/(1-x-x^3), {x, 0, nn}], x]* Range[0, nn]!] (* G. C. Greubel, May 01 2017 *) PROG (PARI) x='x+O('x^30); Vec(serlaplace( 1/(1-x-x^3) )) \\ G. C. Greubel, May 01 2017 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1-x-x^3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 07 2019 (Sage) m = 30; T = taylor(1/(1-x-x^3), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 07 2019 (GAP) a:=[1, 2, 12];; for n in [4..30] do a[n]:=n*a[n-1]+n*(n-1)*(n-2) *a[n-3]; od; Concatenation([1], a); # G. C. Greubel, May 07 2019 CROSSREFS Sequence in context: A018931 A062119 A181966 * A052833 A277490 A296975 Adjacent sequences:  A052553 A052554 A052555 * A052557 A052558 A052559 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 STATUS approved

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Last modified January 28 13:11 EST 2020. Contains 331321 sequences. (Running on oeis4.)