A142243 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..45.

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

EXAMPLE

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;

MATHEMATICA