A142243 Triangle T(n,k) = binomial(2*n,k) *binomial(2*n-2*k,n-k), read by rows; 0<=k<=n.

1, 2, 2, 6, 8, 6, 20, 36, 30, 20, 70, 160, 168, 112, 70, 252, 700, 900, 720, 420, 252, 924, 3024, 4620, 4400, 2970, 1584, 924, 3432, 12936, 22932, 25480, 20020, 12012, 6006, 3432, 12870, 54912, 110880, 141120, 127400, 87360, 48048, 22880, 12870, 48620

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Sep 17 2008

Keywords

• nonn
• tabl

Comments

Row sums are s(n) = 1, 4, 20, 106, 580, 3244,,...

Examples

			1;
2, 2;
6, 8, 6;
20, 36, 30, 20;
70, 160, 168, 112, 70;
252, 700, 900, 720, 420, 252;
924, 3024, 4620, 4400, 2970, 1584, 924;
3432, 12936, 22932, 25480, 20020, 12012, 6006, 3432;
12870, 54912, 110880, 141120, 127400, 87360, 48048, 22880, 12870;
48620, 231660, 525096, 753984, 771120, 599760, 371280, 190944, 87516, 48620';
184756, 972400, 2445300, 3912480, 4476780, 3907008, 2713200, 1550400, 755820, 335920, 184756;
		

Crossrefs

Cf. A062344.

Programs

Mathematica

t[n_, m_] = (Binomial[2*n, m]*Binomial[2*(n - m), (n - m)]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

Conjecture for row sums: 2*(n+1)*(2*n+1)*s(n) +(-81*n^2+19*n-8)*s(n-1) +10*(51*n^2-77*n+30)*s(n-2) -500*(n-1)*(2*n-3)*s(n-3)=0. - R. J. Mathar, Sep 13 2013