A065420 - OEIS

%I #10 Sep 02 2018 15:02:14

%S 2,6,6,12,30,12,20,90,90,20,30,210,380,210,30,42,420,1190,1190,420,42,

%T 56,756,3080,4830,3080,756,56,72,1260,6972,15750,15750,6972,1260,72,

%U 90,1980,14280,43890,63252,43890,14280,1980,90,110,2970,27060,108570,212982

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

%C T(n,k) = T(n,n-k). - _Robert Israel_, Jan 08 2017

%H Robert Israel, <a href="/A065420/b065420.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)

%F From _Robert Israel_, Jan 08 2017:  (Start)

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

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

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

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

%p seq(seq(T(n,k),k=0..n),n=0..10); # _Robert Israel_, Jan 08 2017

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

%Y Cf. A002378, A033487.

%K nonn,easy,tabl

%O 0,1

%A Gary W. Adamson, Nov 15 2001

%E More terms from _Naohiro Nomoto_, Nov 22 2001