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A256019 a(n) = Sum_{i=1..n-1} (i^3 * a(i)), a(1)=1. 2
1, 1, 9, 252, 16380, 2063880, 447861960, 154064514240, 79035095805120, 57695619937737600, 57753315557675337600, 76927416322823549683200, 133007502822161917402252800, 292350491203111894450151654400, 802502098352542150265666291328000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..15.

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.

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}]}]

CROSSREFS

Cf. A001710, A051893, A158621, A256020.

Sequence in context: A303050 A194790 A158621 * A135484 A178186 A212290

Adjacent sequences:  A256016 A256017 A256018 * A256020 A256021 A256022

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 13 2015

STATUS

approved

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Last modified April 23 21:25 EDT 2019. Contains 322388 sequences. (Running on oeis4.)