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A046652 Triangle of rooted planar maps, read by rows. 2

%I

%S 1,2,2,3,8,7,4,21,34,30,5,44,114,160,143,6,80,308,609,806,728,7,132,

%T 715,1908,3315,4256,3876,8,203,1482,5185,11420,18444,23256,21318,9,

%U 296,2814,12600,34520,67856,104652,130416,120175,10,414,4984,27965,93924,221300,404016,603801,746350,690690,11,560,8343,57584,234066,654336,1394505,2418372,3533145,4341480,4032015

%N Triangle of rooted planar maps, read by rows.

%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> [Annotated scanned copy]

%e Triangle begins:

%e 1,

%e 2,2,

%e 3,8,7,

%e 4,21,34,30,

%e 5,44,114,160,143,

%e 6,80,308,609,806,728,

%e ...

%p 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

%t 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-Fran├žois Alcover_, Jan 20 2014, after Herman Jamke *)

%Y A091665 is the same triangle with rows reversed and has much more information.

%K tabl,nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)