A256020 a(n) = Sum_{i=1..n-1} (i^4 * a(i)), a(1)=1.

1, 1, 17, 1394, 358258, 224269508, 290877551876, 698687879606152, 2862524242746404744, 18783884080901907930128, 187857624693099981209210128, 2750611340756369924865254694176, 57039427373264843131930786593127712, 1629160124635190449534207126672913710144

Offset: 1

Author

Vaclav Kotesovec, Mar 13 2015

Keywords

• nonn

Crossrefs

Cf. A001710, A051893, A255434, A256019.

Programs

Mathematica

Clear[a]; a[1]=1; a[n_]:= a[n] = Sum[i^4*a[i],{i,1,n-1}]; Table[a[n],{n,1,15}]
Flatten[{1,1, Table[Product[(i^4 + 1), {i,2,n-1}],{n,3,15}]}]
Join[{1},FoldList[Times,Range[15]^4+1]/2] (* Harvey P. Dale, Jul 29 2018 *)

Formula

a(n) = Product_{i=2..n-1} (i^4 + 1), for n>2.

a(n) ~ (cosh(Pi/sqrt(2))^2 * sin(Pi/sqrt(2))^2 + cos(Pi/sqrt(2))^2 * sinh(Pi/sqrt(2))^2) / (2*Pi^2) * ((n-1)!)^4.

a(n) = A255434(n-1)/2.