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A375220 T(n,k) is the number of permutations of the multiset {1, 1, 2, 2, ..., n, n} with k occurrences of fixed pairs (j,j), where T(n,k), n >= 2, 0 <= k <= n-2 is a triangle read by rows.

%I A375220 #17 Aug 19 2024 17:44:50
%S A375220 5,74,15,2193,296,30,101644,10965,740,50,6840085,609864,32895,1480,75,
%T A375220 630985830,47880595,2134524,76755,2590,105,76484389121,5047886640,
%U A375220 191522380,5692064,153510,4144,140,11792973495032,688359502089,22715489880,574567140,12807144,276318,6216,180
%N A375220 T(n,k) is the number of permutations of the multiset {1, 1, 2, 2, ..., n, n} with k occurrences of fixed pairs (j,j), where T(n,k), n >= 2, 0 <= k <= n-2 is a triangle read by rows.
%F A375220 T(n,n) = 1, T(n,n-1) = 0 (terms not in DATA),
%F A375220 T(n,n-2) = 5*n*(n-1)/2 = 5*A000217(n-1) = A028895(n-1),
%F A375220 Sum_{j=0..n-2} T(n,j) = (2*n)!/(2^n) - 1 = A000680(n) - 1,
%F A375220 Sum_{j=1..n-2} T(n,j) = A375223(n) - 1.
%e A375220 The triangle begins
%e A375220           5,
%e A375220          74,       15,
%e A375220        2193,      296,      30,
%e A375220      101644,    10965,     740,    50,
%e A375220     6840085,   609864,   32895,  1480,   75,
%e A375220   630985830, 47880595, 2134524, 76755, 2590, 105
%o A375220 (PARI) \\ using functions mima and a375219 from A375219, row n of triangle:
%o A375220 a375219(n,sizeb=2)
%Y A375220 Cf. A000217, A000680, A028895, A116218, A374980 (column 0), A375222 (column 1), A375223.
%Y A375220 Cf. A375219 (similar for triples in the multiset).
%K A375220 nonn,tabl
%O A375220 2,1
%A A375220 _Hugo Pfoertner_, Aug 08 2024