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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 (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

Table of n, a(n) for n=0..50.

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;

52,75,100,100,75,5;

...

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

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

N. J. A. Sloane.

EXTENSIONS

Edited by Vladeta Jovovic, Sep 17 2003

STATUS

approved

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Last modified October 23 13:15 EDT 2018. Contains 316528 sequences. (Running on oeis4.)