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

0,3

Links

Table of n, a(n) for n=0..65.

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

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 *)

Crossrefs

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

Sequence in context: A208919 A347580 A259569 * A063007 A331430 A347678

Adjacent sequences: A046648 A046649 A046650 * A046652 A046653 A046654

Keyword

tabl,nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved