OFFSET
7,1
COMMENTS
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
REFERENCES
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).
LINKS
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.
MAPLE
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
MATHEMATICA
V[r_, k_] := Module[{a, t}, a = k - 1;
For[t = k - 2, t >= 1, t--, a = a*(r + t)/(t + 2)];
For[t = 3, t <= k + 1, t++, a = a*(r - t)/(k - t + 2)];
a];
A002060[n_] := V[n, n - 5];
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Hugo Pfoertner, Dec 26 2021
STATUS
approved