A124847 - OEIS

%I #17 Nov 14 2019 09:11:36

%S 1,1,3,1,6,6,1,9,18,10,1,12,36,40,15,1,15,60,100,75,21,1,18,90,200,

%T 225,126,28,1,21,126,350,525,441,196,36,1,24,168,560,1050,1176,784,

%U 288,45,1,27,216,840,1890,2646,2352,1296,405,55,1,30,270,1200,3150,5292,5880

%N Triangle read by rows: T(n,k) = k(k+1)*binomial(n-1, k-1)/2 (1 <= k <= n).

%C Sum of row n gives A049611(n).

%C Triangle is P*A, where P is the Pascal triangle written as a lower triangular matrix and C is the diagonal matrix of the triangular numbers 1, 3, 6, 10, ....

%e First few rows of the triangle:

%e   1;

%e   1,   3;

%e   1,   6,   6;

%e   1,   9,  18,  10;

%e   1,  12,  36,  40,  15;

%e   1,  15,  60, 100,  75,  21;

%e   ...

%e Sum of row 3 = 38 = (1 + 9 + 18 + 10) = A049611(3).

%p T:=(n,k)->k*(k+1)*binomial(n-1,k-1)/2: for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

%Y Cf. A049611.

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Nov 10 2006

%E Edited by _N. J. A. Sloane_, Nov 24 2006