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A127777 A127773 * A002260 as infinite lower triangular matrices.

%I A127777 #12 Jun 18 2021 08:40:50
%S A127777 1,3,6,6,12,18,10,20,30,40,15,30,45,60,75,21,42,63,84,105,126,28,56,
%T A127777 84,112,140,168,196,36,72,108,144,180,216,252,288,45,90,135,180,225,
%U A127777 270,315,360,405,55,110,165,220,275,330,385,440,495,550,66,132,198
%N A127777 A127773 * A002260 as infinite lower triangular matrices.
%C A127777 Triangular number transform of A002260.
%C A127777 Swapped order of the factors: A002260 * A127773 = A127778.
%H A127777 Harvey P. Dale, <a href="/A127777/b127777.txt">Table of n, a(n) for n = 1..1000</a>
%F A127777 T(n,k) = k*binomial(n+1,n-1) = Sum_{i=1..k} i*binomial(k,i)*binomial(n+2-k,n-i), 1 <= k <= n. - _Mircea Merca_, Apr 11 2012
%e A127777 First few rows of the triangle:
%e A127777    1;
%e A127777    3,  6;
%e A127777    6, 12, 18;
%e A127777   10, 20, 30, 40;
%e A127777   15, 30, 45, 60, 75;
%e A127777   ...
%p A127777 T(n,k):=piecewise(k<=n,k*binomial(n+1,n-1),n<k,0) # _Mircea Merca_, Apr 11 2012
%t A127777 Table[k*Binomial[n+1,n-1],{n,20},{k,n}]//Flatten (* _Harvey P. Dale_, Oct 26 2016 *)
%Y A127777 Cf. A000217, A127773, A000537 (row sums), A127778.
%K A127777 nonn,tabl,easy
%O A127777 1,2
%A A127777 _Gary W. Adamson_, Jan 28 2007
%E A127777 More terms from _Harvey P. Dale_, Oct 26 2016