A375219 -id:A375219 - cp's OEIS frontend

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.

5, 74, 15, 2193, 296, 30, 101644, 10965, 740, 50, 6840085, 609864, 32895, 1480, 75, 630985830, 47880595, 2134524, 76755, 2590, 105, 76484389121, 5047886640, 191522380, 5692064, 153510, 4144, 140, 11792973495032, 688359502089, 22715489880, 574567140, 12807144, 276318, 6216, 180

Offset: 2

Hugo Pfoertner, Aug 08 2024

			The triangle begins
          5,
         74,       15,
       2193,      296,      30,
     101644,    10965,     740,    50,
    6840085,   609864,   32895,  1480,   75,
  630985830, 47880595, 2134524, 76755, 2590, 105

Cf. A000217, A000680, A028895, A116218, A374980 (column 0), A375222 (column 1), A375223.

Cf. A375219 (similar for triples in the multiset).

\\ using functions mima and a375219 from A375219, row n of triangle:
a375219(n,sizeb=2)

T(n,n) = 1, T(n,n-1) = 0 (terms not in DATA),
T(n,n-2) = 5*n*(n-1)/2 = 5*A000217(n-1) = A028895(n-1),
Sum_{j=0..n-2} T(n,j) = (2*n)!/(2^n) - 1 = A000680(n) - 1,
Sum_{j=1..n-2} T(n,j) = A375223(n) - 1.

cp's OEIS Frontend

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.

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