A059949 Number of 8-block bicoverings of an n-set.

0, 0, 0, 0, 0, 535, 51640, 2771685, 114713760, 4127125695, 136631722920, 4292250804985, 130278290187760, 3863262740532195, 112733098867629240, 3252644718804860925, 93093809127731630400, 2649006256251644780935

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..100

Formula

a(n) = (1/8!)*(28^n - 8*21^n - 28*16^n + 56*15^n + 168*11^n - 224*10^n + 210*8^n - 840*7^n + 700*6^n - 840*5^n + 1925*4^n + 1064*3^n - 5460*2^n + 4368).

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.: -5*x^6*(3390266880*x^8 -3368778336*x^7 +1334596314*x^6 -268312855*x^5 +27919999*x^4 -1171492*x^3 -29534*x^2 +4331*x -107) / ((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)*(15*x -1)*(16*x -1)*(21*x -1)*(28*x -1)). - Colin Barker, Jul 08 2013

Crossrefs

Column k=8 of A059443.

Cf. A002718.

Sequence in context: A252536 A067723 A252275 * A256088 A250709 A077076

Adjacent sequences: A059946 A059947 A059948 * A059950 A059951 A059952

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 14 2001

Status

approved