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 A077612 #19 Jan 22 2023 02:36:40
%S A077612 0,0,0,12,48,720,4320,60480,483840,7257600,72576000,1197504000,
%T A077612 14370048000,261534873600,3661488230400,73229764608000,
%U A077612 1171676233728000,25609494822912000,460970906812416000,10948059036794880000,218961180735897600000,5620003638888038400000
%N A077612 Number of adjacent pairs of form (even,even) among all permutations of {1,2,...,n}.
%F A077612 a(n) = floor(n/2)*floor(n/2-1)*(n-1)!. Proof: There are floor(n/2)*floor(n/2-1) pairs (r, s) with r and s even and distinct. For each pair, there are n-1 places it can occur in a permutation and (n-2)! possible arrangements of the other numbers.
%F A077612 a(n) = A110660(n+2) * A000142(n-1). - _Michel Marcus_, Aug 29 2013
%F A077612 Sum_{n>=4} 1/a(n) = CoshIntegral(1) - gamma - 3*e + 8 = A099284 - A001620 - 3*A001113 + 8. - _Amiram Eldar_, Jan 22 2023
%t A077612 a[n_] := Floor[n/2]*Floor[n/2 - 1]*(n - 1)!; Array[a, 25] (* _Amiram Eldar_, Jan 22 2023 *)
%o A077612 (PARI) a(n) = n\2 * (n\2-1)*(n-1)! ; \\ _Michel Marcus_, Aug 29 2013
%Y A077612 Cf. A000142, A077611, A077613, A110660.
%Y A077612 Cf. A001113, A001620, A099284.
%K A077612 nonn
%O A077612 1,4
%A A077612 _Leroy Quet_, _Frank Ruskey_ and _Dean Hickerson_, Nov 11 2002