A059947 Number of 6-block bicoverings of an n-set.

0, 0, 0, 3, 256, 7255, 149660, 2681063, 44659776, 714287535, 11154475420, 171673613023, 2618246526896, 39701554817015, 599773397512380, 9038881598035383, 136004367641775616, 2044264589908169695, 30705868769902628540, 461006369270166660143, 6919274132365824549936

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

• Georg Fischer, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (48,-932,9550,-56319,194762,-382908,387000,-151200).

Crossrefs

Column k=6 of A059443.

Cf. A002718.

Programs

Mathematica

CoefficientList[Series[x^4*(16800*x^4-11362*x^3+2237*x^2-112*x-3) / ((1-x)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(15*x-1)), {x, 0, 21}], x] (* Georg Fischer, May 18 2019 *)

PARI

a(n)=(1/6!)*(15^n-6*10^n-15*7^n+30*6^n+60*4^n-50*3^n-180*2^n+240) \\ Georg Fischer, May 18 2019

Formula

a(n) = (1/6!)*(15^n - 6*10^n - 15*7^n + 30*6^n + 60*4^n - 50*3^n - 180*2^n + 240).

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

G.f.: x^4*(16800*x^4-11362*x^3+2237*x^2-112*x-3) / ((1-x)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(15*x-1)). [Colin Barker, Jan 11 2013; corrected by Georg Fischer, May 18 2019]

Extensions

More terms from Colin Barker, Jan 11 2013