A065420 Triangle T(n,k) = binomial(n+2,k+1)*(binomial(n+2,k+1)-1), n >=0, 0 <= k <= n.

2, 6, 6, 12, 30, 12, 20, 90, 90, 20, 30, 210, 380, 210, 30, 42, 420, 1190, 1190, 420, 42, 56, 756, 3080, 4830, 3080, 756, 56, 72, 1260, 6972, 15750, 15750, 6972, 1260, 72, 90, 1980, 14280, 43890, 63252, 43890, 14280, 1980, 90, 110, 2970, 27060, 108570, 212982

Offset: 0

Author

Gary W. Adamson, Nov 15 2001

Keywords

• nonn
• easy
• tabl

Comments

T(n,k) = T(n,n-k). - Robert Israel, Jan 08 2017

Examples

			2; 6,6; 12,30,12; 20,90,90,20; ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)

Crossrefs

Cf. A002378, A033487.

Programs

Maple

T:= (n,k) -> binomial(n+2,k+1)*(binomial(n+2,k+1)-1):
seq(seq(T(n,k),k=0..n),n=0..10); # Robert Israel, Jan 08 2017

Mathematica

#(#-1)&/@Table[Binomial[n+2,k+1],{n,0,10},{k,0,n}]//Flatten (* Harvey P. Dale, Sep 02 2018 *)

Formula

From Robert Israel, Jan 08 2017: (Start)

T(n,0) = (n+1)*(n+2) = A002378(n+1).

T(n,1) = n*(n+1)*(n+2)*(n+3)/4 = A033487(n). (End)

Extensions

More terms from Naohiro Nomoto, Nov 22 2001