A120493 - OEIS

%I #13 Aug 12 2015 15:07:11

%S 1,1,1,2,4,2,5,15,15,5,14,56,84,56,14,42,210,420,420,210,42,132,792,

%T 1980,2640,1980,792,132,428,2996,8988,14980,14980,8988,2996,428,1416,

%U 11328,39648,79296,99120,79296,39648,11328,1416

%N Triangle T(n,k) read by rows ; multiply row n of Pascal's triangle (A007318) by A024175(n).

%C Triangle given by [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

%F T(n,k)=A007318(n,k)*A024175(n).

%F T(n,k)=6*T(n-1,k)+6*T(n-1,k-1)-10*T(n-2,k)-20*T(n-2,k-1)-10*T(n-2,k-2)+4*T(n-3,k)+12*T(n-3,k-1)+12*T(n-3,k-2)+4*T(n-3,k-3) for n>3, T(0,0)=T(1,0)=T(1,1)=1, T(2,0)=T(2,2)=2, T(2,1)=4, T(3,0)=T(3,3)=5, T(3,1)=T(3,2)=15, T(n,k)=0 if k<0 or if k>n. - _Philippe Deléham_, Nov 22 2013

%F G.f.: (-1 +5*x +5*x*y -6*x^2 -12*x^2*y -6*x^2*y^2 +x^3 +3*x^3*y +3*x^3*y^2 +x^3*y^3)/( (-1+2*x+2*x*y) *(2*x^2*y^2+4*x^2*y+2*x^2-4*x*y-4*x+1) ). - _R. J. Mathar_, Aug 12 2015

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 4, 2;

%e 5, 15, 15, 5;

%e 14, 56, 84, 56, 14;

%e 42, 210, 420, 420, 210, 42;

%e 132, 792, 1980, 2640, 1980, 792, 132;

%e 428, 2996, 8988, 14980, 14980, 8988, 2996, 428;

%e 1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416 ;...

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Aug 05 2006