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1, 3, 12, 59, 339, 2210, 16033, 127643, 1103372, 10269643, 102225363, 1082190554, 12126858113, 143268057587, 1778283994284, 23120054355195, 314017850216371, 4444972514600178, 65435496909148513, 999907522895563403
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refs;
listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Number of symmetric positions of non-attacking rooks on upper-diagonal part of 2n X 2n chessboard.
Number of length-n restricted growth strings (RGS) [s(0),s(1),...,s(n-1)] where s(0)=0 and s(k)<=2+max(prefix) for k>=1. [From Joerg Arndt, Apr 25 2010]
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LINKS
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Table of n, a(n) for n=1..20.
Joerg Arndt, Fxtbook, section 17.3.4, pp. 364-366
J. Quaintance, Letter representations of rectangular m x n x p proper arrays
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FORMULA
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Binomial transform of A002872 (sorting numbers).
E.g.f.: exp(x+exp(x)+exp(2*x)/2-3/2) = exp(x+sum(j=1,2, (exp(j*x)-1)/j ) ). [Joerg Arndt, Apr 29 2011]
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EXAMPLE
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For n=0 there is one empty string (term a(0)=0 not included here); for n=1 there is one string [0]; for n=2 there are 3 strings [00], [01], and [02];
for n=3 there are a(3)=12 strings (in lexicographic order):
1:[000],
2:[001],
3:[002],
4:[010],
5:[011],
6:[012],
7:[013],
8:[020],
9:[021],
10:[022],
11:[023],
12:[024].
[From Joerg Arndt, Apr 25 2010]
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MATHEMATICA
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Table[Sum[ Binomial[n, k] A002872[[k + 1]], {k, 0, n}], {n, 0, 24}]
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PROG
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(Pari) x='x+O('x^66); /* that many terms */
egf=exp(x+exp(x)+exp(2*x)/2-3/2); /* = 1 +3*x +6*x^2 +59/6*x^3 +113/8*x^4 +... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 29 2011 */
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CROSSREFS
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Cf. A002872, A080107.
Sequence in context: A192768 A179325 A064856 * A196710 A196711 A101054
Adjacent sequences: A080334 A080335 A080336 * A080338 A080339 A080340
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen, Mar 18 2003
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EXTENSIONS
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Comment corrected by Wouter Meeussen, Aug 14 2009
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STATUS
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approved
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