A059950 Number of 9-block bicoverings of an n-set.

0, 0, 0, 0, 0, 15, 8456, 954213, 66253552, 3622342095, 172672602432, 7557346901841, 312733696544984, 12456923582109435, 483124650731622328, 18383758048494864909, 689931203330381971296, 25630900118611348761735, 945025181750878420241744, 34647077709586498046291817

Offset

1,6

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n)=(1/9!)*(36^n -9*28^n -36*22^n +72*21^n +252*16^n -336*15^n +378*12^n -1512*11^n +1260*10^n -1890*8^n +5040*7^n -4536*6^n +7560*5^n -8820*4^n -11256*3^n +28728*2^n -19152).

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).

G.f.: x^6*(69766476595200*x^11 -73112128911360*x^10 +31807557729984*x^9 -7437208397056*x^8 +993276127572*x^7 -70229555428*x^6 +1198328731*x^5 +199609307*x^4 -16366808*x^3 +505224*x^2 -5351*x -15) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(15*x -1)*(16*x -1)*(21*x -1)*(22*x -1)*(28*x -1)*(36*x -1)). - Colin Barker, Jul 09 2013

Crossrefs

Column k=9 of A059443.

Cf. A002718.

Sequence in context: A334835 A206295 A074488 * A198979 A249967 A308156

Adjacent sequences: A059947 A059948 A059949 * A059951 A059952 A059953

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 14 2001

Status

approved