A375222 a(n) is the number of permutations of the multiset 1,1, 2,2, ..., n,n such that exactly one pair k,k stays at its initial locations 2k-1, 2k.

1, 0, 15, 296, 10965, 609864, 47880595, 5047886640, 688359502089, 117929734950320, 24798753695076471, 6280419381186155160, 1885582606127524251805, 662239984799385248609976, 268999138538324585872798395, 125133475474486312764311243744, 66091677106419135401506827779985

Offset: 1

Author

Hugo Pfoertner, Aug 05 2024

Keywords

• nonn

Comments

1

Examples

			a(3) = 15: The permutations with one stable pair are
  [1, 1, 2, 3, 2, 3], [1, 1, 2, 3, 3, 2], [1, 1, 3, 2, 2, 3], [1, 1, 3, 2, 3, 2],
  [1, 1, 3, 3, 2, 2], [1, 2, 1, 2, 3, 3], [1, 2, 2, 1, 3, 3], [1, 3, 2, 2, 1, 3],
  [1, 3, 2, 2, 3, 1], [2, 1, 1, 2, 3, 3], [2, 1, 2, 1, 3, 3], [2, 2, 1, 1, 3, 3],
  [3, 1, 2, 2, 1, 3], [3, 1, 2, 2, 3, 1], [3, 3, 2, 2, 1, 1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..238

Crossrefs

Cf. A000680 (all permutations of this multiset), A375223 (at least one stable pair), A374980.

Programs

PARI

a375222(n) = {my(p=vector(2*n,i,1+(i-1)\2), m1=0); forperm (p, q, my(m=0); for (k=1, n, if (q[2*k-1]==k && q[2*k]==k, m++)); m1+=(m==1)); m1}

Formula

a(n) = n * A374980(n-1). - Alois P. Heinz, Aug 05 2024

Extensions

a(8) onwards from Alois P. Heinz, Aug 05 2024