A256019 a(n) = Sum_{i=1..n-1} (i^3 * a(i)), a(1)=1.

1, 1, 9, 252, 16380, 2063880, 447861960, 154064514240, 79035095805120, 57695619937737600, 57753315557675337600, 76927416322823549683200, 133007502822161917402252800, 292350491203111894450151654400, 802502098352542150265666291328000

Offset: 1

Author

Vaclav Kotesovec, Mar 13 2015

Keywords

• nonn

Comments

a(n) = A158621(n-1) for n > 2. - Georg Fischer, Oct 23 2018

Crossrefs

Cf. A001710, A051893, A158621, A256020.

Programs

Mathematica

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

Formula

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

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

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