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A052759
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E.g.f.: x^3*log(1/(1-x)).
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6
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0, 0, 0, 0, 24, 60, 240, 1260, 8064, 60480, 518400, 4989600, 53222400, 622702080, 7925299200, 108972864000, 1609445376000, 25406244864000, 426824913715200, 7602818775552000, 143111882833920000, 2838385676206080000, 59157933040926720000, 1292600836944248832000
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OFFSET
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0,5
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COMMENTS
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Previous name was: A simple grammar.
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LINKS
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FORMULA
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E.g.f.: x^3*log(-1/(-1+x)).
Recurrence: a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-n^2+2*n+3)*a(n)+(-2+n)*a(n+1) = 0.
Sum_{n>=4} (-1)^n/a(n) = 3/2 - 4/e. - Amiram Eldar, Aug 20 2022
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MAPLE
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spec := [S, {B=Cycle(Z), S=Prod(B, Z, Z, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Join[{0, 0, 0, 0}, Table[n!/(n - 3), {n, 4, 30}]] (* Vincenzo Librandi, Jul 08 2015 *)
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PROG
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(PARI) a(n) = if (n <= 3, 0, n!/(n-3)); \\ Michel Marcus, Jul 08 2015
(Magma) [n le 3 select 0 else Factorial(n)/(n-3): n in [0..30]]; // Vincenzo Librandi, Jul 08 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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