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A052897
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A simple grammar.
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5
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1, 2, 8, 44, 304, 2512, 24064, 261536, 3173888, 42483968, 621159424, 9841950208, 167879268352, 3065723549696, 59651093528576, 1231571119812608, 26883546193002496, 618463501807058944
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 873
N. J. A. Sloane, Transforms
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FORMULA
| E.g.f.: exp(2*x/(1-x)) - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2001
Recurrence: {a(0)=1, a(1)=2, (n^2+n)*a(n)+(-4-2*n)*a(n+1)+a(n+2)}
LAH transform of A000079: a(n) = Sum_{k=0..n) 2^k*n!/k!*binomial(n-1, k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 17 2003
a(n)=n!*L(n,-1,-2) - Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 16 2006 [Here L(n,a,x) is the n-th generalized Laguerre polynomial with parameter a, evaluated at x. L(n,a,x) is 1 if n=0, a+1-x if n=1 and otherwise (2*n+a-1-x)/n*L(n-1,a,x)-(n+a-1)/n*L(n-2,a,x). - Peter Luschny, Nov 20 2011]
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MAPLE
| L := proc(n, a, x) if n=0 then 1 elif n=1 then a+1-x else (2*n+a-1-x)/n*L(n-1, a, x) - (n+a-1)/n*L(n-2, a, x) fi end: A052897 := n -> n!*L(n, -1, -2): seq(A052897(n), n=0..17); # Peter Luschny, Nov 20 2011
spec := [S, {B=Set(C), C=Sequence(Z, 1 <= card), S=Prod(B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| Range[0, 19]! CoefficientList[ Series[E^(2*x/(1 - x)), {x, 0, 19}], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2007
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PROG
| (PARI) a=Vec(exp(2*x/(1-x))); for(n=2, #a-1, a[n+1]*=n!); a \\ Charles R Greathouse IV, Nov 20 2011
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CROSSREFS
| Row sums of A059110.
Cf. A025168.
Sequence in context: A112912 A124467 A075792 * A137984 A191810 A172109
Adjacent sequences: A052894 A052895 A052896 * A052898 A052899 A052900
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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