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 A033306 Triangle of coefficients of ordered cycle-index polynomials: T(n,k) = binomial(n,k)*Bell(k)*Bell(n-k). 5
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80. LINKS FORMULA E.g.f.: exp(exp(x*y)+exp(x)-2). EXAMPLE 1;    1,  1;    2,  2,   2;    5,  6,   6,   5;   15, 20,  24,  20, 15;   52, 75, 100, 100, 75, 52;   ... MAPLE 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 MATHEMATICA 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 *) CROSSREFS 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 KEYWORD nonn,tabl,easy AUTHOR EXTENSIONS Edited by Vladeta Jovovic, Sep 17 2003 STATUS approved

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Last modified April 18 03:09 EDT 2021. Contains 343072 sequences. (Running on oeis4.)