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A052700
Expansion of e.g.f. x*(1-x)/(1-3*x).
1
0, 1, 4, 36, 432, 6480, 116640, 2449440, 58786560, 1587237120, 47617113600, 1571364748800, 56569130956800, 2206196107315200, 92660236507238400, 4169710642825728000, 200146110855634944000, 10207451653637382144000
OFFSET
0,3
LINKS
FORMULA
E.g.f.: x*(1-x)/(1-3*x)
D-finite recurrence: a(1)=1, a(0)=0, a(2)=4, a(n) = 3*n*a(n-1).
a(n) = 2*3^(n-2)*n! = 2*A153647(n-2), n>1.
MAPLE
spec := [S, {S=Prod(Z, Sequence(Prod(Sequence(Z), Union(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[2*3^(n-2)*n! -2*Boole[n==0]/9 + Boole[n==1]/3, {n, 0, 30}] (* G. C. Greubel, May 31 2022 *)
With[{nn=30}, CoefficientList[Series[x (1-x)/(1-3x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 19 2022 *)
PROG
(SageMath) [0, 1]+[2*3^(n-2)*factorial(n) for n in (2..30)] # G. C. Greubel, May 31 2022
CROSSREFS
Cf. A153647.
Sequence in context: A371679 A132864 A294050 * A167540 A374857 A136224
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved