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A198064 Triangle read by rows (n >= 0, 0 <= k <= n, m = 4); T(n,k) = Sum{j=0..m} Sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).

%I A198064 #5 Mar 30 2012 17:27:13
%S A198064 0,1,1,16,5,16,81,31,31,81,256,121,80,121,256,625,341,211,211,341,625,
%T A198064 1296,781,496,405,496,781,1296,2401,1555,1031,781,781,1031,1555,2401,
%U A198064 4096,2801,1936,1441,1280,1441,1936,2801,4096,6561,4681,3355,2511,2101
%N A198064 Triangle read by rows (n >= 0, 0 <= k <= n, m = 4); T(n,k) = Sum{j=0..m} Sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).
%F A198064 T(n,k) = k^4-2*k^3*n+4*k^2*n^2-3*k*n^3+n^4.
%F A198064 T(n,0) = T(n,n) = n^m = n^4 = A000583(n).
%F A198064 T(2n,n) = (m+1)n^m = 5n^4.
%F A198064 T(2n+1,n+1) = (n+1)^(m+1)-n^(m+1) = (n+1)^5-n^5 = A022521(n).
%F A198064 Sum{k=0..n} T(n,k) = (16n^5+30n^4+15n^3-n)/30.
%F A198064 T(n+1,k+1)C(n,k)^5/(k+1)^4 = A197654(n,k).
%e A198064 [0]                      0
%e A198064 [1]                     1, 1
%e A198064 [2]                  16, 5, 16
%e A198064 [3]                81, 31, 31, 81
%e A198064 [4]            256, 121, 80, 121, 256
%e A198064 [5]         625, 341, 211, 211, 341, 625
%e A198064 [6]     1296, 781, 496, 405, 496, 781, 1296
%e A198064 [7] 2401, 1555, 1031, 781, 781, 1031, 1555, 2401
%p A198064 A198064 := (n,k) -> k^4-2*k^3*n+4*k^2*n^2-3*k*n^3+n^4:
%Y A198064 Cf. A057427, A003056, A073254, A198063, A198065.
%K A198064 nonn,tabl
%O A198064 0,4
%A A198064 _Peter Luschny_, Oct 26 2011