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%I #7 Oct 09 2013 09:33:25
%S 1,1,4,1,0,1,9,4,5,1,0,1,21,19,12,9,7,1,0,1,52,57,53,47,16,16,9,1,0,1,
%T 127,178,202,154,120,85,20,25,11,1,0,1,313,543,664,636,525,310,233,
%U 133,24,36,13,1,0,1,778,1591,2204,2355,2007,1621,1076,549,404,191,28,49,15
%N Table read by rows where row n consists of 2n terms representing k-matches described in A098813.
%C For a string of letters of length k, say abc...def, let f(k) be the string of length k-1 consisting of the adjacent pairs ab, bc, cd, ..., de, ef. Given n, let U be the string of length 2n consisting of n 1's followed by n 2's: 11...122...2. Then T(n,k) = number of the C(2n,n) permutations V of U such that f(U) and f(V) agree in exactly k places, 0<=k<=2n-1.
%e Table begins:
%e 1: 1,1,
%e 2: 4,1,0,1,
%e 3: 9,4,5,1,0,1,
%e 4: 21,19,12,9,7,1,0,1,
%e 5: 52,57,53,47,16,16,9,1,0,1,
%e 6: 127,178,202,154,120,85,20,25,11,1,0,1,
%e 7: 313,543,664,636,525,310,233,133,24,36,13,1,0,1,
%e 8: 778,1591,2204,2355,2007,1621,1076,549,404,191,28,49,15,1,0,1,
%e 9: 1941,4598,7091,8223,8036,6722,4721,3457,1911,901,645,259,32,64,17,1,0,1
%Y First column is A051292(n+1); second column is A098813; row sums = A000984.
%K nonn,tabf
%O 1,3
%A _Zerinvary Lajos_ and _Ray Chandler_, Oct 26 2004
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