OFFSET
0,2
LINKS
W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.
W. G. Brown, Enumeration of non-separable planar maps [Annotated scanned copy]
EXAMPLE
Triangle begins:
1;
2, 2;
3, 8, 7;
4, 21, 34, 30;
5, 44, 114, 160, 143;
6, 80, 308, 609, 806, 728;
...
MAPLE
T := proc(n, k) if k<=n then k*sum((2*j-k+1)*(j-1)!*(3*n-k-j)!/(j-k+1)!/(j-k)!/(2*k-j-1)!/(n-j)!, j=k..min(n, 2*k-1))/(2*n-k+1)! else 0 fi end: seq(seq(T(n, n-k+1), k=1..n), n=1..11); # Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008
MATHEMATICA
t[n_, k_] := If[k <= n, k*Sum[(2*j-k+1)*(j-1)!*(3*n-k-j)!/(j-k+1)!/(j-k)!/(2*k-j-1)!/(n-j)!, {j, k, Min[n, 2*k-1]}]/(2*n-k+1)!, 0]; Table[t[n, k], {n, 1, 11}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 20 2014, after Herman Jamke *)
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008
STATUS
approved