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 A110104 #10 Oct 24 2023 07:28:29
%S A110104 1,4,3760,23504320,567399078400,37518268781593600,
%T A110104 5543744611870143078400,1599334510537656091623424000,
%U A110104 818296434784062385011283591168000
%N A110104 a(n) is the number of coverings of 1..n by cyclic words of length 3n, such that each value from 1 to n appears precisely twice. That is, the union of all the letters in all of the words of a given covering is the multiset {1,1,2,2,...,n,n}. No repeats of words are allowed in a given covering.
%C A110104 P-recursive.
%F A110104 Differential equation satisfied by egf: sum a(n)t^3n/(3n!) {F(0) = 1, (-2+4*t^6+16*t^3)*(d/dt)F(t) + 4*t^4*(d^2/dt^2)F(t) + t^2*(4+12*t^3+t^6)*F(t)}.
%F A110104 Recurrence: {a(0) = 1, (40320 + 328752*n + 1816668*n^3 + 1102248*n^5 + 398034*n^6 + 1818369*n^4 + 1063116*n^2 + 78732*n^7 + 6561*n^8)*a(n) +(508608*n + 161280 + 453600*n^3 + 34992*n^5 + 2916*n^6 + 173340*n^4 + 661104*n^2)*a(n+1) + (12320 + 19980*n + 12096*n^2 + 3240*n^3 + 324*n^4)*a(n+2) - 2*a(n+3), a(1) = 4, a(2) = 3760}.
%F A110104 a(n) ~ 2^n * 3^(4*n + 1/2) * n^(4*n) / exp(4*n). - _Vaclav Kotesovec_, Oct 24 2023
%e A110104 a(1)=4: {123, 132} {112, 233} {113, 322} {133, 122}
%t A110104 RecurrenceTable[{(40320 + 328752*n + 1816668*n^3 + 1102248*n^5 + 398034*n^6 + 1818369*n^4 + 1063116*n^2 + 78732*n^7 + 6561*n^8) * a[n] + (508608*n + 161280 + 453600*n^3 + 34992*n^5 + 2916*n^6 + 173340*n^4 + 661104*n^2) * a[n + 1] + (12320 + 19980*n + 12096*n^2 + 3240*n^3 + 324*n^4) * a[n + 2] - 2*a[n + 3] == 0, a[0] == 1, a[1] == 4, a[2] == 3760}, a, {n, 0, 15}] (* _Vaclav Kotesovec_, Oct 24 2023 *)
%Y A110104 Cf. A052502, A110105, A110106, A108242.
%K A110104 easy,nonn
%O A110104 0,2
%A A110104 _Marni Mishna_, Jul 11 2005