A059948 Number of 7-block bicoverings of an n-set.

0, 0, 0, 0, 40, 3306, 131876, 3961356, 103290096, 2488179582, 57162274972, 1274774473632, 27887396866472, 602352276704178, 12899161619186388, 274612697648135028, 5822592730060070368, 123107330974129584294

Offset: 1

Author

Vladeta Jovovic, Feb 14 2001

Keywords

• easy
• nonn

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

Crossrefs

Column k=7 of A059443.

Cf. A002718.

Formula

a(n)=(1/7!) * (21^n -7*15^n -21*11^n +42*10^n +105*7^n -140*6^n +105*5^n -420*4^n +35*3^n +1050*2^n -1050).

The number of m-block bicoverings of an n-set is [x^m*y^n] 1/n!*exp(-x-1/2*x^2*(exp(y)-1)) * sum(i>=0, x^i/i! * exp(binomial(i, 2)*y) ) where [x^m*y^n] extracts the coefficient of x^m*y^n, see Goulden/Jackson p.203.

G.f.: 2*x^5*(5197500*x^6-4601880*x^5+1501221*x^4-219455*x^3+12587*x^2+47*x-20) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(11*x-1)*(15*x-1)*(21*x-1)). - Colin Barker, Jul 07 2013