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 A321233 #58 Apr 26 2023 18:34:01
%S A321233 0,4,128,4992,241664,14131200,972521472,77138231296,6935178903552,
%T A321233 697359579217920,77576992194560000,9461629052252061696,
%U A321233 1255632936007234486272,180144800985155488448512,27786422394606966747955200,4585649599904345055716966400,806288164205933489807717040128
%N A321233 a(n) is the number of reflectable bases of the root system of type D_n.
%C A321233 The root systems of type D_n are only defined for n >= 4. See chapter 3 of the Humphreys reference. Sequence extended to n=1 using formula/recurrence.
%D A321233 J. E. Humphreys, Introduction to Lie algebras and representation theory, 2nd ed, Springer-Verlag, New York, 1972.
%H A321233 S. Azam, M. B. Soltani, M. Tomie and Y. Yoshii, <a href="https://doi.org/10.4171/PRIMS/55-4-2">A graph theoretical classification for reflectable bases</a>, PRIMS, Vol 55 no 4, (2019), 689-736.
%F A321233 E.g.f.: Sum_{m>=2} (1/(4*m)) (Sum_{k>=1} k^(k-1)*(4*x)^k/k!)^m.
%F A321233 a(n) = 2^n*A320064(n).
%F A321233 a(n) = (n-1)*4^(n-1)*A001863(n). - _M. F. Hasler_, Dec 09 2018
%t A321233 Rest[With[{m = 25}, CoefficientList[Series[Sum[Sum[j^(j - 1)*(4*x)^j/j!, {j, 1, m + 1}]^k/(4*k), {k, 2, m}], {x, 0, m}], x]*Range[0, m]!]] (* _G. C. Greubel_, Dec 09 2018 *)
%o A321233 (PARI) a(n)={n!*polcoef(sum(m=2, n, (sum(k=1, n, k^(k-1)*(4*x)^k/k!) + O(x^(n-m+2)))^m/(4*m)), n)} \\ _Andrew Howroyd_, Nov 01 2018
%o A321233 (PARI) A321233(n)=A001863(n)*(n-1)*4^(n-1) \\ _M. F. Hasler_, Dec 09 2018
%o A321233 (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (&+[ (&+[ j^(j-1)*(4*x)^j/Factorial(j) :j in [1..m+3]])^k/(4*k) :k in [2..m+2]]) )); [0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // _G. C. Greubel_, Dec 09 2018
%o A321233 (Python)
%o A321233 from math import comb
%o A321233 def A321233(n): return 0 if n<2 else ((sum(comb(n,k)*(n-k)**(n-k)*k**k for k in range(1,(n+1>>1)))<<1) + (0 if n&1 else comb(n,m:=n>>1)*m**n))//n<<(n-1<<1) # _Chai Wah Wu_, Apr 26 2023
%Y A321233 Cf. A000435, A320064.
%K A321233 nonn
%O A321233 1,2
%A A321233 _Masaya Tomie_, Nov 01 2018