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%I #16 Mar 08 2020 00:23:23
%S 1,1,2,1,6,6,1,12,26,24,1,20,75,120,110,1,30,174,416,594,546,1,42,350,
%T 1176,2289,3094,2856,1,56,636,2880,7322,12768,16728,15504,1,72,1071,
%U 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
%N Triangle of rooted planar maps.
%H W. G. Brown, <a href="http://dx.doi.org/10.4153/CJM-1963-056-7">Enumeration of non-separable planar maps</a>, Canad. J. Math., 15 (1963), 526-545.
%H W. G. Brown, <a href="/A000087/a000087.pdf">Enumeration of non-separable planar maps</a>
%p 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
%t 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 *)
%Y A091599 is the same triangle with rows reversed and has much more information.
%K tabl,nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 19 2008
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