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

1,3

Links

Table of n, a(n) for n=1..14.

Formula

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.

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 *)

Crossrefs

Cf. A001710, A051893, A256019.

Sequence in context: A007410 A203229 A269791 * A072160 A376097 A078814

Adjacent sequences: A256017 A256018 A256019 * A256021 A256022 A256023

Keyword

nonn

Author

Vaclav Kotesovec, Mar 13 2015

Status

approved