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

2,1

Links

Table of n, a(n) for n=2..37.

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),

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.

Example

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

Prog

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

Crossrefs

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

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

Sequence in context: A131958 A051156 A092826 * A334258 A322446 A065894

Adjacent sequences: A375198 A375200 A375219 * A375221 A375222 A375223

Keyword

nonn,tabl,new

Author

Hugo Pfoertner, Aug 08 2024

Status

approved