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 A002060 Number of partitions of a n-gon into (n-5) parts. (Formerly M3691 N1509) 4

%I M3691 N1509

%S 4,60,550,4004,25480,148512,813960,4263600,18573816

%N Number of partitions of a n-gon into (n-5) parts.

%C a(n) = V(r=n,k=n-5), 4th subdiagonal of the triangle of V on page 240.

%C It appears that V(r=15,k=10) in the Cayley table is an error, so the sequence was intended to be 4, 60, 550, 4004, 25480, 148512, 813960, 4263600, 21573816, 106234700, 511801290, 2421810300, 11289642000, 51967090560, 236635858800... - _R. J. Mathar_, Nov 26 2011

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H A. Cayley, <a href="http://dx.doi.org/10.1112/plms/s1-22.1.237">On the partitions of a polygon</a>, Proc. London Math. Soc., 22 (1891), 237-262 = Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.

%p V := proc(r,k)

%p local a ,t;

%p a := k-1;

%p for t from k-2 to 1 by -1 do

%p a := a*(r+t)/(t+2) ;

%p end do:

%p for t from 3 to k+1 do

%p a := a*(r-t)/(k-t+2) ;

%p end do:

%p a ;

%p end proc:

%p A002060 := proc(n)

%p V(n,n-5) ;

%p end proc:

%p seq(A002060(n),n=7..25) ; # _R. J. Mathar_, Nov 26 2011

%Y Cf. A002058, A002059.

%K nonn

%O 7,1

%A _N. J. A. Sloane_

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Last modified May 10 16:34 EDT 2021. Contains 343775 sequences. (Running on oeis4.)