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A059951 Number of 10-block bicoverings of an n-set. 30
0, 0, 0, 0, 0, 0, 420, 154637, 20368816, 1775801814, 124151410020, 7596257673279, 426319554841752, 22564352299016528, 1146221298547133380, 56531610963314602401, 2728475248127447671008, 129586638359127411410442, 6080467290450346517206500, 282689089820505452872162403 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

LINKS

Table of n, a(n) for n=1..20.

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

Cf. A002718, A059443, A003462, A059945-A059950.

Sequence in context: A035846 A223941 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

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Last modified September 15 20:35 EDT 2019. Contains 327087 sequences. (Running on oeis4.)