cp's OEIS Frontend

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.

%I A375223 #17 Aug 05 2024 23:35:43
%S A375223 1,1,16,327,11756,644315,50094570,5245258879,711662648968,
%T A375223 121448713262139,25460198594647070,6431844723440756015,
%U A375223 1927058631207405670716,675631849624828664480107,274032655042818911590547266,127312224468011793400981895295,67167619760422081463964260973200
%N 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.
%H A375223 Alois P. Heinz, <a href="/A375223/b375223.txt">Table of n, a(n) for n = 1..239</a>
%F A375223 a(n) = Sum_{j=1..n} binomial(n,j) * A374980(n-j). - _Alois P. Heinz_, Aug 05 2024
%e A375223 a(3) = 16: The 15 permutations with one stable pair (see A375222) and the starting configuration [1, 1, 2, 2, 3, 3].
%o A375223 (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}
%Y A375223 Cf. A000680 (all permutations of this multiset), A375222 (exactly one stable pair), A374980.
%K A375223 nonn
%O A375223 1,3
%A A375223 _Hugo Pfoertner_, Aug 05 2024
%E A375223 a(8) onwards from _Alois P. Heinz_, Aug 05 2024