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 A243667 #39 Aug 08 2023 07:57:47
%S A243667 1,1,6,50,484,5105,56928,660112,7878940,96159476,1194532794,
%T A243667 15053992178,191993403476,2473358617150,32137897641232,
%U A243667 420698195672700,5542894551818268,73447821835338348,978178443083177880,13086377223959022952,175785879063917657688
%N A243667 Number of Sylvester classes of 4-packed words of degree n.
%C A243667 See Novelli-Thibon (2014) for precise definition.
%H A243667 Seiichi Manyama, <a href="/A243667/b243667.txt">Table of n, a(n) for n = 0..865</a>
%H A243667 J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962 [math.CO], 2014. See Eq. (185), p. 47 and Fig. 17.
%F A243667 Novelli-Thibon give an explicit formula in Eq. (182).
%F A243667 From _Seiichi Manyama_, Jul 26 2020: (Start)
%F A243667 G.f. A(x) satisfies: A(x) = 1 - x * A(x)^4 * (1 - 2 * A(x)).
%F A243667 a(n) = (-1)^n * Sum_{k=0..n} (-2)^k * binomial(n,k) * binomial(4*n+k+1,n)/(4*n+k+1).
%F A243667 a(n) = ( (-1)^n / (4*n+1) ) * Sum_{k=0..n} (-2)^(n-k) * binomial(4*n+1,k) * binomial(5*n-k,n-k). (End)
%F A243667 a(n) ~ 2^(9*n - 15) * sqrt(436289 + 2793997/sqrt(41)) / (sqrt(Pi) * n^(3/2) * (29701 - 4633*sqrt(41))^(n - 1/2)). - _Vaclav Kotesovec_, Jul 31 2021
%F A243667 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(5*n-k,n-1-k) for n > 0. - _Seiichi Manyama_, Aug 08 2023
%t A243667 P[n_, m_, x_] := 1/(m n + 1) Sum[Binomial[m n + 1, k] Binomial[(m + 1) n - k, n - k] (1 - x)^k x^(n - k), {k, 0, n}];
%t A243667 a[n_] := P[n, 4, 2];
%t A243667 a /@ Range[20] (* _Jean-François Alcover_, Jan 28 2020 *)
%o A243667 (PARI) a(n) = my(A=1+x*O(x^n)); for(i=0, n, A=1-x*A^4*(1-2*A)); polcoeff(A, n); \\ _Seiichi Manyama_, Jul 26 2020
%o A243667 (PARI) a(n) = (-1)^n*sum(k=0, n, (-2)^k*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1)); \\ _Seiichi Manyama_, Jul 26 2020
%o A243667 (PARI) a(n) = (-1)^n*sum(k=0, n, (-2)^(n-k)*binomial(4*n+1, k)*binomial(5*n-k, n-k))/(4*n+1); \\ _Seiichi Manyama_, Jul 26 2020
%Y A243667 Column k=4 of A336573.
%Y A243667 Cf. A243668, A336572.
%K A243667 nonn
%O A243667 0,3
%A A243667 _N. J. A. Sloane_, Jun 14 2014
%E A243667 More terms from _Jean-François Alcover_, Jan 28 2020
%E A243667 a(0)=1 prepended by _Seiichi Manyama_, Jul 25 2020