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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.
0
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
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.
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, A028895, 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
KEYWORD
nonn,tabl
AUTHOR
Hugo Pfoertner, Aug 08 2024
STATUS
approved