A059951 Number of 10-block bicoverings of an n-set.

0, 0, 0, 0, 0, 0, 420, 154637, 20368816, 1775801814, 124151410020, 7596257673279, 426319554841752, 22564352299016528, 1146221298547133380, 56531610963314602401, 2728475248127447671008, 129586638359127411410442, 6080467290450346517206500, 282689089820505452872162403

Offset

1,7

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

Formula

a(n) = (1/10!)*(45^n - 10*36^n - 45*29^n + 90*28^n + 360*22^n - 480*21^n + 630*17^n - 2520*16^n + 2100*15^n - 3780*12^n + 10080*11^n - 6552*10^n - 3150*9^n + 18900*8^n - 31500*7^n + 28560*6^n - 46620*5^n + 27720*4^n + 85560*3^n - 146160*2^n + 83520).

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.: -x^7*(5467233152463667200*x^14 -6460773223081605120*x^13 +3312489509664336576*x^12 -965946275708647680*x^11 +175045400422088532*x^10 -19853467917718628*x^9 +1255863452001343*x^8 -11591551437545*x^7 -5424120630669*x^6 +520759916751*x^5 -24697320639*x^4 +659527325*x^3 -8843563*x^2 +25697*x +420) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(15*x -1)*(16*x -1)*(17*x -1)*(21*x -1)*(22*x -1)*(28*x -1)*(29*x -1)*(36*x -1)*(45*x -1)). - Colin Barker, Jul 09 2013

Crossrefs

Column k=10 of A059443.

Cf. A002718.

Sequence in context: A223941 A360537 A046167 * A225992 A028683 A198163

Adjacent sequences: A059948 A059949 A059950 * A059952 A059953 A059954

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 14 2001

Extensions

More terms from Colin Barker, Jul 09 2013

Status

approved