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A033306
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Triangle of coefficients of ordered cycle-index polynomials: T(n,k) = binomial(n,k)*Bell(k)*Bell(n-k).
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5
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1, 1, 1, 2, 2, 2, 5, 6, 6, 5, 15, 20, 24, 20, 15, 52, 75, 100, 100, 75, 52, 203, 312, 450, 500, 450, 312, 203, 877, 1421, 2184, 2625, 2625, 2184, 1421, 877, 4140, 7016, 11368, 14560, 15750, 14560, 11368, 7016, 4140, 21147, 37260, 63144, 85260, 98280, 98280, 85260, 63144, 37260, 21147
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80.
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LINKS
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Table of n, a(n) for n=0..54.
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FORMULA
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E.g.f.: exp(exp(x*y)+exp(x)-2).
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EXAMPLE
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1;
1, 1;
2, 2, 2;
5, 6, 6, 5;
15, 20, 24, 20, 15;
52, 75, 100, 100, 75, 52;
...
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MAPLE
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A033306 := proc(n, k)
if k < 0 or k > n then
0;
else
binomial(n, k)*combinat[bell](k)*combinat[bell](n-k) ;
end if;
end proc: # R. J. Mathar, Mar 21 2013
# second Maple program:
b:= proc(n) option remember; expand(`if`(n>0, add(
(x^j+1)*b(n-j)*binomial(n-1, j-1), j=1..n), 1))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n)):
seq(T(n), n=0..10); # Alois P. Heinz, Aug 30 2019
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MATHEMATICA
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t[n_, k_] := Binomial[n, k] * BellB[k] * BellB[n-k]; Table[t[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014 *)
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CROSSREFS
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Cf. A000110, row sums give A001861.
Columns include A000110 and A052889.
Sequence in context: A066835 A123953 A097006 * A136347 A279515 A260338
Adjacent sequences: A033303 A033304 A033305 * A033307 A033308 A033309
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Edited by Vladeta Jovovic, Sep 17 2003
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STATUS
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approved
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