A256019 - OEIS

%I #14 Oct 23 2018 09:27:53

%S 1,1,9,252,16380,2063880,447861960,154064514240,79035095805120,

%T 57695619937737600,57753315557675337600,76927416322823549683200,

%U 133007502822161917402252800,292350491203111894450151654400,802502098352542150265666291328000

%N a(n) = Sum_{i=1..n-1} (i^3 * a(i)), a(1)=1.

%C a(n) = A158621(n-1) for n > 2. - _Georg Fischer_, Oct 23 2018

%F Product_{i=2..n-1} (i^3 + 1), for n>2.

%F a(n) ~ cosh(sqrt(3)*Pi/2) / (2*Pi) * ((n-1)!)^3.

%F a(n) = A255433(n-1)/2.

%t Clear[a]; a[1]=1; a[n_]:= a[n] = Sum[i^3*a[i],{i,1,n-1}]; Table[a[n],{n,1,20}]

%t Flatten[{1, Table[FullSimplify[Cosh[Sqrt[3]*Pi/2] * Gamma[n+1] * Gamma[n-1/2 - I*Sqrt[3]/2] * Gamma[n-1/2 + I*Sqrt[3]/2] / (2*Pi)],{n,2,20}]}]

%Y Cf. A001710, A051893, A158621, A256020.

%K nonn

%O 1,3

%A _Vaclav Kotesovec_, Mar 13 2015