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A120493 Triangle T(n,k) read by rows ; multiply row n of Pascal's triangle (A007318) by A024175(n).

%I A120493 #13 Aug 12 2015 15:07:11
%S A120493 1,1,1,2,4,2,5,15,15,5,14,56,84,56,14,42,210,420,420,210,42,132,792,
%T A120493 1980,2640,1980,792,132,428,2996,8988,14980,14980,8988,2996,428,1416,
%U A120493 11328,39648,79296,99120,79296,39648,11328,1416
%N A120493 Triangle T(n,k) read by rows ; multiply row n of Pascal's triangle (A007318) by A024175(n).
%C A120493 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 A120493 T(n,k)=A007318(n,k)*A024175(n).
%F A120493 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 A120493 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 A120493 Triangle begins:
%e A120493 1;
%e A120493 1, 1;
%e A120493 2, 4, 2;
%e A120493 5, 15, 15, 5;
%e A120493 14, 56, 84, 56, 14;
%e A120493 42, 210, 420, 420, 210, 42;
%e A120493 132, 792, 1980, 2640, 1980, 792, 132;
%e A120493 428, 2996, 8988, 14980, 14980, 8988, 2996, 428;
%e A120493 1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416 ;...
%K A120493 nonn,tabl
%O A120493 0,4
%A A120493 _Philippe Deléham_, Aug 05 2006