7,1

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

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

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

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

Table of n, a(n) for n=7..15.

A. Cayley, On the partitions of a polygon, Proc. London Math. Soc., 22 (1891), 237-262 = Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.

V := proc(r, k)

        local a , t;

        a := k-1;

        for t from k-2 to 1 by -1 do

                a := a*(r+t)/(t+2) ;

        end do:

        for t from 3 to k+1 do

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

        end do:

        a ;

end proc:

A002060 := proc(n)

        V(n, n-5) ;

end proc:

seq(A002060(n), n=7..25) ; # R. J. Mathar, Nov 26 2011

Cf. A002058, A002059.

Sequence in context: A234952 A112041 A210425 * A247739 A007220 A034866

Adjacent sequences:  A002057 A002058 A002059 * A002061 A002062 A002063

nonn

N. J. A. Sloane

approved