A125091 - OEIS

%I #9 Nov 11 2019 21:49:50

%S 1,2,4,3,12,10,4,24,40,20,5,40,100,100,35,6,60,200,300,210,56,7,84,

%T 350,700,735,392,84,8,112,560,1400,1960,1568,672,120,9,144,840,2520,

%U 4410,4704,3024,1080,165,10,180,1200,4200,8820,11760,10080,5400,1650,220,11

%N Triangle read by rows: T(n,k) = (1/6)*k*(k+1)*(k+2)*binomial(n,k) (1 <= k <= n).

%C T(n,n) = n*(n+1)*(n+2)/6 = A000292(n).

%C Sum_{k=1..n} T(n,k) = 2^n*n*(n+2)*(n+7)/48 = A055585(n-1).

%e Triangle starts:

%e   1;

%e   2,   4;

%e   3,  12,  10;

%e   4,  24,  40,  20;

%e   5,  40, 100, 100,  35;

%e   6,  60, 200, 300, 210,  56;

%e   7,  84, 350, 700, 735, 392,  84;

%p T:=(n,k)->k*(k+1)*(k+2)*binomial(n,k)/6: for n from 1 to 11 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

%t Flatten[Table[(k(k+1)(k+2)Binomial[n,k])/6,{n,20},{k,n}]] (* _Harvey P. Dale_, Jan 23 2016 *)

%Y Cf. A055585.

%Y Cf. A000292.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Nov 19 2006

%E Edited by _N. J. A. Sloane_, Dec 04 2006