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A059443
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Triangle T(n,k) (n >= 2) giving number of bicoverings of an n-set with k blocks.
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32
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1, 4, 4, 13, 39, 25, 3, 40, 280, 472, 256, 40, 121, 1815, 6185, 7255, 3306, 535, 15, 364, 11284, 70700, 149660, 131876, 51640, 8456, 420, 1093, 68859, 759045, 2681063, 3961356, 2771685, 954213, 154637, 9730, 105
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OFFSET
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2,2
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COMMENTS
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The rows seem to have irregular lengths.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #40.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
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Table of n, a(n) for n=2..38.
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FORMULA
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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).
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EXAMPLE
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[1], [4, 4], [13, 39, 25, 3], [40, 280, 472, 256, 40], [121, 1815, 6185, 7255, 3306, 535, 15], [364, 11284, 70700, 149660, 131876, 51640, 8456, 420], [1093, 68859, 759045, 2681063, 3961356, 2771685, 954213, 154637, 9730, 105], ...
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MATHEMATICA
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nmax = 8; imax = 2*(nmax - 2); egf := E^(-x - 1/2*x^2*(E^y - 1))*Sum[(x^i/i!)*E^(Binomial[i, 2]*y), {i, 0, imax}]; fx = CoefficientList[ Series[ egf , {y, 0, imax}], y]*Range[0, imax]!; row[n_] := Drop[ CoefficientList[ Series[fx[[n + 1]], {x, 0, imax}], x], 3]; Table[ row[n], {n, 2, nmax}] // Flatten (* Jean-François Alcover, Sep 21 2012 *)
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PROG
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Contribution from Gerald McGarvey, Dec 03 2009: (Start)
(PARI) \ps 22;
s = 8; pv = vector(s); for(n=1, s, pv[n]=round(polcoeff(f(x, y), n, y)*n!));
for(n=1, s, for(m=3, poldegree(pv[n], x), print1(polcoeff(pv[n], m), ", "))) (End)
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CROSSREFS
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Leading diagonal is A003462. Row sums are A002718. Cf. A059945-A059950.
Sequence in context: A147824 A019081 A219454 * A097335 A117187 A138767
Adjacent sequences: A059440 A059441 A059442 * A059444 A059445 A059446
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KEYWORD
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tabf,nonn,nice,changed
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AUTHOR
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N. J. A. Sloane, Feb 01 2001
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EXTENSIONS
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More terms and additional comments from Vladeta Jovovic, Feb 14 2001
a(37) corrected by Gerald McGarvey, Dec 03 2009
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STATUS
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approved
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