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 A089468 #14 Jan 12 2025 20:28:57
%S A089468 1,3,15,110,1083,13482,203569,3618540,74058105,1715620148,44384718879,
%T A089468 1268498827752,39692276983555,1349678904881400,49556966130059553,
%U A089468 1954156038072106448,82363978221026323761,3695194039210436996400
%N A089468 Hyperbinomial transform of A089467 and also the 2nd hyperbinomial transform of A089466.
%C A089468 See A088956 for the definition of the hyperbinomial transform.
%F A089468 a(n) = Sum_{k=0..n} (n-k+1)^(n-k-1)*C(n, k)*A089467(k).
%F A089468 a(n) = Sum_{k=0..n} 2*(n-k+2)^(n-k-1)*C(n, k)*A089466(k).
%F A089468 a(n) = Sum_{m=0..n} (Sum_{j=0..m} C(m, j)*C(n, n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!.
%F A089468 E.g.f.: (LambertW(-x)^2*exp(-1/2*LambertW(-x)^2))/(x^2*(1+LambertW(-x))). - _Vladeta Jovovic_, Oct 26 2004
%F A089468 a(n) ~ exp(3/2)*n^n. - _Vaclav Kotesovec_, Jul 09 2013
%t A089468 CoefficientList[Series[(LambertW[-x]^2*E^(-1/2*LambertW[-x]^2))/(x^2*(1+LambertW[-x])), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jul 09 2013 *)
%o A089468 (PARI) a(n)=if(n<0,0,sum(m=0,n,sum(j=0,m,binomial(m,j)*binomial(n,n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!))
%Y A089468 Cf. A089466, A089467, A088956.
%K A089468 nonn
%O A089468 0,2
%A A089468 _Paul D. Hanna_, Nov 08 2003