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

Author

Hugo Pfoertner, Aug 08 2024

Keywords

• nonn
• tabl

Examples

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

Crossrefs

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

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

Programs

PARI

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

Formula

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.