A143083 - OEIS

%I #19 Jul 15 2017 15:07:05

%S 3,10,70,21,252,1386,36,660,5148,25740,55,1430,15015,97240,461890,78,

%T 2730,37128,302328,1763580,8112468,105,4760,81396,813960,5720330,

%U 31201800,140408100,136,7752,162792,1961256,16343800,104303160,542911320,2404321560

%N A triangle of coefficients: T(n,m) = (2*n + 2*m + 3)! / (2*(2*m + 1)!*(2*n + 1)!).

%C Row sums begin: 3, 80, 1659, 31584, 575630, 10218312, 178230451, 3070011776, 52387009722, 887453729920, 14946680628638, ...

%H Maryam Mirzakhani, <a href="http://www.ams.org/journals/jams/2007-20-01/S0894-0347-06-00526-1/S0894-0347-06-00526-1.pdf">Weil-Petersson volumes and intersection theory on the moduli space of curves</a>, Journal of the American Mathematical Society, Vol. 20(1), Jan. 2007, p. 18.

%e {3},

%e {10, 70},

%e {21, 252, 1386},

%e {36, 660, 5148, 25740},

%e {55, 1430, 15015, 97240, 461890},

%e {78, 2730, 37128, 302328, 1763580, 8112468},

%e {105, 4760, 81396, 813960, 5720330, 31201800, 140408100},

%e {136, 7752, 162792, 1961256, 16343800, 104303160, 542911320, 2404321560},

%e {171, 11970, 302841, 4326300, 42181425, 311375610, 1856277675, 9334424880, 40838108850},

%e {210, 17710, 531300, 8880300, 100150050, 846723150, 5731664400, 32479431600, 159053687100, 689232644100},

%e {253, 25300, 888030, 17168580, 221760825, 2128903920, 16239715800, 103006197360, 561232295910, 2691289372200, 11572544300460}

%p T := (n, m) -> (n+1)*binomial(2*(n+m+1)+1, 2*m+1):

%p for n from 0 to 6 do seq(T(n,m), m=0..n) od; # _Peter Luschny_, Jul 15 2017

%t Table[(2*n + 2*m + 3)!/(2*(2*m + 1)!(2*n + 1)!), {n, 0, 8}, {m, 0, n}] // Flatten

%Y Cf. A014105 (column 0).

%K nonn,tabl

%O 1,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 15 2008

%E Edited by _Peter Luschny_, Jul 15 2017