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A059948 Number of 7-block bicoverings of an n-set. 3
0, 0, 0, 0, 40, 3306, 131876, 3961356, 103290096, 2488179582, 57162274972, 1274774473632, 27887396866472, 602352276704178, 12899161619186388, 274612697648135028, 5822592730060070368, 123107330974129584294 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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)=(1/7!) * (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

CROSSREFS

Column k=7 of A059443.

Cf. A002718.

Sequence in context: A268151 A269824 A178721 * A229604 A045502 A347854

Adjacent sequences:  A059945 A059946 A059947 * A059949 A059950 A059951

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 14 2001

STATUS

approved

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Last modified October 21 17:02 EDT 2021. Contains 348155 sequences. (Running on oeis4.)