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A052571
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E.g.f. x^3/(1-x)^2.
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3
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0, 0, 0, 6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200, 4790016000, 68497228800, 1046139494400, 16999766784000, 292919058432000, 5335311421440000, 102437979291648000, 2067966706950144000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 514
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FORMULA
| E.g.f.: x^3/(-1+x)^2
Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(3)=6, (1-n^2)*a(n)+(-2+n)*a(n+1)=0}
(n-2)*n! (n>1).
a(n)=n*(n+1)*(n+2)*n! - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a(n)=3*A090672(n-2) =6*A005990(n-2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
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MAPLE
| spec := [S, {S=Prod(Z, Z, Z, Sequence(Z), Sequence(Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
[seq (n*(n+1)*(n+2)*n!, n=0..17)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a:=n->add((n!), j=1..n-2):seq(a(n), n=0..21); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
restart: G(x):=x^3/(1-x)^2: f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]
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MATHEMATICA
| Table[Sum[n!, {i, 3, n}], {n, 0, 19}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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PROG
| (MAGMA) [0, 0], [n*(n+1)*(n+2)*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
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CROSSREFS
| Sequence in context: A166152 A049316 A024075 * A052625 A155130 A083233
Adjacent sequences: A052568 A052569 A052570 * A052572 A052573 A052574
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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