A046651 Triangle of rooted planar maps.

1, 1, 2, 1, 6, 6, 1, 12, 26, 24, 1, 20, 75, 120, 110, 1, 30, 174, 416, 594, 546, 1, 42, 350, 1176, 2289, 3094, 2856, 1, 56, 636, 2880, 7322, 12768, 16728, 15504, 1, 72, 1071, 6324, 20475, 44388, 72420, 93024, 86526, 1, 90, 1700, 12740, 51495, 136252, 267240, 417240, 528770, 493350, 1, 110, 2574, 23936, 118734, 378444, 878460, 1610136, 2437149, 3058770, 2861430

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

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

Crossrefs

A091599 is the same triangle with rows reversed and has much more information.

Programs

Maple

T := proc(n, k) if k<=n then k*sum((2*j-k)*(j-1)!*(3*n-j-k-1)!/(j-k)!/(j-k)!/(2*k-j)!/(n-j)!, j=k..min(n, 2*k))/(2*n-k)! else 0 fi end: seq(seq(T(n, n-k+1), k=1..n), n=1..11); # Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 19 2008

Mathematica

t[n_, k_] := If[k <= n, k*Sum[(2*j-k)*(j-1)!*(3*n-j-k-1)!/(j-k)!/(j-k)!/(2*k-j)!/(n-j)!, {j, k, Min[n, 2*k]}]/(2*n-k)!, 0]; Table[Table[t[n, n-k+1], {k, 1, n}], {n, 1, 11}] // Flatten (* Jean-François Alcover, Jan 14 2014, after Herman Jamke *)

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 19 2008