A143083 A triangle of coefficients: T(n,m) = (2*n + 2*m + 3)! / (2*(2*m + 1)!*(2*n + 1)!).

3, 10, 70, 21, 252, 1386, 36, 660, 5148, 25740, 55, 1430, 15015, 97240, 461890, 78, 2730, 37128, 302328, 1763580, 8112468, 105, 4760, 81396, 813960, 5720330, 31201800, 140408100, 136, 7752, 162792, 1961256, 16343800, 104303160, 542911320, 2404321560

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..36.

Maryam Mirzakhani, Weil-Petersson volumes and intersection theory on the moduli space of curves, Journal of the American Mathematical Society, Vol. 20(1), Jan. 2007, p. 18.

Example

{3},
{10, 70},
{21, 252, 1386},
{36, 660, 5148, 25740},
{55, 1430, 15015, 97240, 461890},
{78, 2730, 37128, 302328, 1763580, 8112468},
{105, 4760, 81396, 813960, 5720330, 31201800, 140408100},
{136, 7752, 162792, 1961256, 16343800, 104303160, 542911320, 2404321560},
{171, 11970, 302841, 4326300, 42181425, 311375610, 1856277675, 9334424880, 40838108850},
{210, 17710, 531300, 8880300, 100150050, 846723150, 5731664400, 32479431600, 159053687100, 689232644100},
{253, 25300, 888030, 17168580, 221760825, 2128903920, 16239715800, 103006197360, 561232295910, 2691289372200, 11572544300460}

Maple

T := (n, m) -> (n+1)*binomial(2*(n+m+1)+1, 2*m+1):
for n from 0 to 6 do seq(T(n, m), m=0..n) od; # Peter Luschny, Jul 15 2017

Mathematica

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

Crossrefs

Cf. A014105 (column 0).

Sequence in context: A308814 A342629 A232213 * A002499 A047833 A047834

Adjacent sequences: A143080 A143081 A143082 * A143084 A143085 A143086

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Oct 15 2008

Extensions

Edited by Peter Luschny, Jul 15 2017

Status

approved