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A052649
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E.g.f. (2+x-x^2)/(1-x)^2.
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3
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2, 5, 14, 54, 264, 1560, 10800, 85680, 766080, 7620480, 83462400, 997920000, 12933043200, 180583603200, 2702527027200, 43153254144000, 732297646080000, 13160434839552000, 249692574523392000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(1) is 5 and gives the row number in the table of 0-origin permutations of order 3 in which the first 3 items are reversed. Row 5 of this table is 2 1 0. a(2) is 14 and gives the row number in the table of 0-origin permutations of order 4 in which the first three items are reversed. Row 14 of this table is 2 1 0 3.... a(6) is 10800 and gives the row number in the table of 0-origin permutations of order 8 in which the first 3 items are reversed. Row 10800 of this table is 2 1 0 3 4 5 6 7. Et cetera. - Eugene McDonnell (eemcd(AT)mac.com), Dec 03 2004
a(n) = (n+1)*a(n-1) - 2*A001048(n-1). [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 16 2009]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 596
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FORMULA
| a(n) = (3+2*n)*n!
E.g.f.: -(-x+x^2-2)/(-1+x)^2
Recurrence: a(0)=2, a(1)=5, (-7*n-5-2*n^2)*a(n)+(3+2*n)*a(n+1)=0 for n>=1
a(n) = A129326(n), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2008
a(n)= (n+1)a(n-1) - 2[(n-1)!+(n-2)! ] [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 16 2009]
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MAPLE
| spec := [S, {S=Prod(Sequence(Z), Union(Z, Sequence(Z), Sequence(Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| f[n_] := (3 + 2 n) n!; f[0] = 2; Array[f, 19, 0]
a[n_] := a[n] = a[n - 1]*n (2 n + 3)/(2 n + 1); a[0] = 2; a[1] = 5; Array[ a, 19, 0] ( RGWv *)
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PROG
| (PARI) a(n)=if(n<=1, [2, 5][n+1], a(n-1)*(n*(2*n+3))/(2*n+1) );
for(n=0, 11, print1(a(n), ", ")) /* show terms */
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CROSSREFS
| Sequence in context: A115275 A000679 A081439 * A122594 A047136 A047042
Adjacent sequences: A052646 A052647 A052648 * A052650 A052651 A052652
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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