login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059443 Triangle T(n,k) (n >= 2) giving number of bicoverings of an n-set with k blocks. 32
1, 4, 4, 13, 39, 25, 3, 40, 280, 472, 256, 40, 121, 1815, 6185, 7255, 3306, 535, 15, 364, 11284, 70700, 149660, 131876, 51640, 8456, 420, 1093, 68859, 759045, 2681063, 3961356, 2771685, 954213, 154637, 9730, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

The rows seem to have irregular lengths.

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #40.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

LINKS

Table of n, a(n) for n=2..38.

FORMULA

E.g.f. for m-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i=0..inf} x^i/i!*exp(binomial(i, 2)*y).

EXAMPLE

[1], [4, 4], [13, 39, 25, 3], [40, 280, 472, 256, 40], [121, 1815, 6185, 7255, 3306, 535, 15], [364, 11284, 70700, 149660, 131876, 51640, 8456, 420], [1093, 68859, 759045, 2681063, 3961356, 2771685, 954213, 154637, 9730, 105], ...

MATHEMATICA

nmax = 8; imax = 2*(nmax - 2); egf := E^(-x - 1/2*x^2*(E^y - 1))*Sum[(x^i/i!)*E^(Binomial[i, 2]*y), {i, 0, imax}]; fx = CoefficientList[ Series[ egf , {y, 0, imax}], y]*Range[0, imax]!; row[n_] := Drop[ CoefficientList[ Series[fx[[n + 1]], {x, 0, imax}], x], 3]; Table[ row[n], {n, 2, nmax}] // Flatten (* Jean-Fran├žois Alcover, Sep 21 2012 *)

PROG

Contribution from Gerald McGarvey, Dec 03 2009: (Start)

(PARI) \ps 22;

s = 8; pv = vector(s); for(n=1, s, pv[n]=round(polcoeff(f(x, y), n, y)*n!));

for(n=1, s, for(m=3, poldegree(pv[n], x), print1(polcoeff(pv[n], m), ", "))) (End)

CROSSREFS

Leading diagonal is A003462. Row sums are A002718. Cf. A059945-A059950.

Sequence in context: A147824 A019081 A219454 * A241250 A097335 A117187

Adjacent sequences:  A059440 A059441 A059442 * A059444 A059445 A059446

KEYWORD

tabf,nonn,nice

AUTHOR

N. J. A. Sloane, Feb 01 2001

EXTENSIONS

More terms and additional comments from Vladeta Jovovic, Feb 14 2001

a(37) corrected by Gerald McGarvey, Dec 03 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified October 24 23:00 EDT 2014. Contains 248516 sequences.