The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A059951

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A059951

Number of 10-block bicoverings of an n-set.
(history; published version)

#11 by Alois P. Heinz at Wed Jan 29 19:34:53 EST 2020

STATUS

proposed

approved

#10 by Andrew Howroyd at Wed Jan 29 18:37:32 EST 2020

STATUS

editing

proposed

#9 by Andrew Howroyd at Wed Jan 29 18:26:54 EST 2020

LINKS

Andrew Howroyd, <a href="/A059951/b059951.txt">Table of n, a(n) for n = 1..200</a>

#8 by Andrew Howroyd at Wed Jan 29 18:25:04 EST 2020

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).

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).

CROSSREFS

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

Column k=10 of A059443.

Cf. A002718.

STATUS

approved

editing

#7 by Joerg Arndt at Wed Jul 10 02:43:49 EDT 2013

STATUS

proposed

approved

#6 by Colin Barker at Tue Jul 09 13:31:05 EDT 2013

STATUS

editing

proposed

#5 by Colin Barker at Tue Jul 09 13:30:30 EDT 2013

NAME

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

DATA

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

FORMULA

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

EXTENSIONS

More terms from Colin Barker, Jul 09 2013

STATUS

approved

editing

#4 by Charles R Greathouse IV at Fri May 10 12:44:35 EDT 2013

AUTHOR

_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Feb 14 2001

Discussion

Fri May 10

12:44

OEIS Server: https://oeis.org/edit/global/1911

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

KEYWORD

easy,nonn,new

AUTHOR

Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Feb 14 2001

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

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).

KEYWORD

easy,nonn,new