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A059947
Number of 6-block bicoverings of an n-set.
3
0, 0, 0, 3, 256, 7255, 149660, 2681063, 44659776, 714287535, 11154475420, 171673613023, 2618246526896, 39701554817015, 599773397512380, 9038881598035383, 136004367641775616, 2044264589908169695, 30705868769902628540, 461006369270166660143, 6919274132365824549936
OFFSET
1,4
REFERENCES
I. P. Goulden and D. M.Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
LINKS
Index entries for linear recurrences with constant coefficients, signature (48,-932,9550,-56319,194762,-382908,387000,-151200).
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]
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 *)
PROG
(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
CROSSREFS
Column k=6 of A059443.
Cf. A002718.
Sequence in context: A364876 A045824 A027860 * A203495 A051490 A232545
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 14 2001
EXTENSIONS
More terms from Colin Barker, Jan 11 2013
STATUS
approved