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A052687
Expansion of e.g.f. (1+x-x^3)/((1-x)*(1-x^2)).
1
1, 2, 6, 18, 96, 480, 3600, 25200, 241920, 2177280, 25401600, 279417600, 3832012800, 49816166400, 784604620800, 11769069312000, 209227898880000, 3556874280960000, 70426110763008000, 1338096104497152000
OFFSET
0,2
LINKS
FORMULA
E.g.f.: (1 + x - x^3)/((1-x)*(1-x^2)).
Recurrence: a(0)=1, a(1)=2, a(2)=6, a(3)=18, (n+4)*a(n+2) = (n+2)*a(n+1) + (n+1)*(n+2)*(n+5)*a(n).
a(n) = n! * (2*n + 7 + (-1)^n)/4.
a(n) = n!*A004526(n+4), n>0. - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Prod(Sequence(Z), Union(Z, Sequence(Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[n!*(2*n+7+(-1)^n)/4 -Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Jun 03 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1+x-x^3)/((1-x)*(1-x^2)) ))); // G. C. Greubel, Jun 03 2022
(SageMath) [factorial(n)*(n + 3 + ((n+1)%2))/2 - bool(n==0) for n in (0..30)] # G. C. Greubel, Jun 03 2022
CROSSREFS
Sequence in context: A053505 A000138 A028857 * A302546 A162059 A162060
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved