A375223 a(n) is the number of permutations of the multiset 1,1, 2,2, ..., n,n such that at least one pair k,k stays at its initial locations 2k-1, 2k.

1, 1, 16, 327, 11756, 644315, 50094570, 5245258879, 711662648968, 121448713262139, 25460198594647070, 6431844723440756015, 1927058631207405670716, 675631849624828664480107, 274032655042818911590547266, 127312224468011793400981895295, 67167619760422081463964260973200

Offset: 1

Author

Hugo Pfoertner, Aug 05 2024

Keywords

• nonn

Examples

			a(3) = 16: The 15 permutations with one stable pair (see A375222) and the starting configuration [1, 1, 2, 2, 3, 3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..239

Crossrefs

Cf. A000680 (all permutations of this multiset), A375222 (exactly one stable pair), A374980.

Programs

PARI

a375223(n) = {my (p=vector(2*n,i,1+(i-1)\2), m=0); forperm (p, q, for (j=1, n, if (q[2*j-1]==j && q[2*j]==j, m++; break))); m}

Formula

a(n) = Sum_{j=1..n} binomial(n,j) * A374980(n-j). - Alois P. Heinz, Aug 05 2024

Extensions

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