A057884 - OEIS

%I #5 Nov 01 2013 11:45:19

%S 1,0,1,4,1,1,0,4,2,1,10,4,5,3,1,0,10,8,7,4,1,20,10,14,13,10,5,1,0,20,

%T 20,22,20,14,6,1,35,20,30,34,35,30,19,7,1,0,35,40,50,56,55,44,25,8,1,

%U 56,35,55,70,84,91,85,63,32,9,1,0,56,70,95,120,140,146,129,88,40,10,1

%N A square array based on tetrahedral numbers (A000292) with each term being the sum of 2 consecutive terms in the previous row.

%F T(n, k)=T(n-1, k-1)+T(n, k-1) with T(0, k)=1, T(4, 1)=4, T(0, 2n)=T(4, n) and T(0, 2n+1)=0. Coefficient of x^n in expansion of (1+x)^k/(1-x^2)^4.

%e Rows are (1,0,4,0,10,0,20,...), (1,1,4,4,10,10,20,...), (1,2,5,8,14,20,30,...), (1,3,7,13,22,34,50,...), (1,4,10,20,35,56,84,...) etc.

%Y Rows are A000292 with zeros, A058187 (A000292 with terms duplicated), A006918, A002623, A000292, A000330, A005900, A001845, A008412.

%K easy,nonn,tabl

%O 0,4

%A _Henry Bottomley_, Nov 20 2000