This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374980 #32 Aug 26 2024 16:07:51
%S A374980 1,0,5,74,2193,101644,6840085,630985830,76484389121,11792973495032,
%T A374980 2254432154097861,523368281765512930,145044815855963403985,
%U A374980 47302856057098946329284,17933275902554972391519893,7820842217155394547769452734,3887745712142302082441578104705
%N A374980 Number of multiset permutations of {1, 1, 2, 2, ..., n, n} with no fixed pair (j,j).
%C A374980 Inverse binomial transform of A000680.
%H A374980 Alois P. Heinz, <a href="/A374980/b374980.txt">Table of n, a(n) for n = 0..238</a>
%F A374980 a(n) = Sum_{j=0..n} (-1)^j*binomial(n,j)*A000680(n-j).
%F A374980 a(n) = A116218(n)/2^n.
%F A374980 a(n) mod 2 = 1 - (n mod 2) = A059841(n).
%e A374980 a(2) = 5: 1212, 1221, 2112, 2121, 2211.
%p A374980 a:= proc(n) option remember; `if`(n<3, [1, 0, 5][n+1],
%p A374980 (n-1)*((2*n+1)*a(n-1)+(4*n-3)*a(n-2)+2*(n-2)*a(n-3)))
%p A374980 end:
%p A374980 seq(a(n), n=0..16);
%Y A374980 Cf. A000166, A000459, A000680, A059841, A116218, A375222, A375223.
%Y A374980 Column k=2 of A375694.
%K A374980 nonn
%O A374980 0,3
%A A374980 _Alois P. Heinz_, Aug 05 2024