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 A089467 #12 Jan 12 2025 23:56:13
%S A089467 1,2,8,52,478,5706,83824,1461944,29510268,676549450,17361810016,
%T A089467 492999348348,15345359136232,519525230896322,19005788951346240,
%U A089467 747102849650454256,31404054519248544016,1405608808807797838866,66741852193123060505728,3350816586986433907218500,177352811048578736727396576
%N A089467 Hyperbinomial transform of A089466 and also the inverse hyperbinomial transform of A089468.
%C A089467 See A088956 for the definition of the hyperbinomial transform.
%F A089467 a(n) = Sum_{k=0..n} (n-k+1)^(n-k-1)*C(n, k)*A089466(k).
%F A089467 a(n) = Sum_{k=0..n} -(n-k-1)^(n-k-1)*C(n, k)*A089468(k).
%F A089467 a(n) = Sum_{m=0..n} (Sum_{j=0..m} C(m, j)*C(n, n-m-j)*n^(n-m-j)*(m+j)!/(-2)^j)/m!.
%F A089467 a(n) ~ exp(1/2) * n^n. - _Vaclav Kotesovec_, Oct 11 2020
%t A089467 Flatten[{1, Table[Sum[Sum[Binomial[m, j] * Binomial[n, n-m-j] * n^(n-m-j) * (m+j)! / (-2)^j / m!, {j,0,m}], {m,0,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Oct 11 2020 *)
%o A089467 (PARI) a(n)=if(n<0,0,sum(m=0,n,sum(j=0,m,binomial(m,j)*binomial(n,n-m-j)*n^(n-m-j)*(m+j)!/(-2)^j)/m!))
%Y A089467 Cf. A089466, A089468, A088956.
%K A089467 nonn
%O A089467 0,2
%A A089467 _Paul D. Hanna_, Nov 08 2003
%E A089467 More terms from _Michel Marcus_, Jan 12 2025