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 A089465 #11 Oct 11 2020 04:47:07
%S A089465 1,4,23,178,1763,21504,313585,5342068,104376201,2304582544,
%T A089465 56807530871,1547599725720,46202052688603,1500629138909632,
%U A089465 52697989385197137,1990117967149595824,80440669725095395025,3465573101368534916928
%N A089465 3rd hyperbinomial transform of A001858; also the hyperbinomial transform of A089462.
%C A089465 A001858 enumerates forests of labeled trees with n nodes and shifts 1 place left under the hyperbinomial transform.
%H A089465 G. C. Greubel, <a href="/A089465/b089465.txt">Table of n, a(n) for n = 0..385</a>
%F A089465 a(n) = Sum_{k=0..n} 3*(n-k+3)^(n-k-1)*C(n, k)*A001858(k).
%F A089465 a(n) = Sum_{m=0..(n+1)} ( Sum_{j=0..m} C(m, j)*C(n, n-m-j+1)*(n+3)^(n-m-j+1)*(m+j)!/(-2)^j )/m!.
%F A089465 a(n) ~ 3 * exp(7/2) * n^(n-1). - _Vaclav Kotesovec_, Oct 11 2020
%t A089465 Table[Sum[Sum[Binomial[m, j]*Binomial[n, n - m - j + 1]*(n + 3)^(n - m - j + 1)*(m + j)!/(-2)^j, {j, 0, m}]/m!, {m, 0, n + 1}], {n, 0, 50}] (* _G. C. Greubel_, Nov 18 2017 *)
%o A089465 (PARI) a(n)=if(n<0,0,sum(m=0,n+1,sum(j=0,m,binomial(m,j)*binomial(n,n-m-j+1)*(n+3)^(n-m-j+1)*(m+j)!/(-2)^j)/m!))
%Y A089465 Cf. A001858, A089462, A089463.
%K A089465 nonn
%O A089465 0,2
%A A089465 _Paul D. Hanna_, Nov 05 2003