A059946 Number of 5-block bicoverings of an n-set.

0, 0, 0, 25, 472, 6185, 70700, 759045, 7894992, 80736625, 817897300, 8241325565, 82783813112, 830046591465, 8313655213500, 83215436364085, 832626645756832, 8329096006484705, 83307920631515300, 833180902353754605, 8332418928963358152, 83327847634888960345

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

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (26,-255,1210,-2924,3384,-1440).

Crossrefs

Column k=5 of A059443.

Cf. A002718.

Programs

Mathematica

With[{c=(1/5!)},Table[c(10^n-5 6^n-10 4^n+20 3^n+30 2^n-60),{n,20}]]  (* Harvey P. Dale, Apr 21 2011 *)

PARI

a(n) = {(1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60)} \\ Andrew Howroyd, Jan 29 2020

Formula

a(n) = (1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60).

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

G.f.: x^4*(288*x^2-178*x+25) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(10*x-1)). - Colin Barker, Jan 11 2013

Extensions

More terms from Colin Barker, Jan 11 2013