OFFSET
1,3
FORMULA
a(n) = Product_{i=2..n-1} (i^2+1), for n>2. - Vladeta Jovovic, Nov 26 2002
From Vaclav Kotesovec, Mar 13 2015: (Start)
For n > 1, a(n) = A101686(n-1)/2.
a(n) ~ (n-1)!^2 * sinh(Pi)/(2*Pi).
(End)
a(n) = sinh(Pi)*Gamma(n-I)*Gamma(n+I)/(2*Pi) for n>1. - Peter Luschny, Oct 19 2016
MAPLE
a := n -> `if`(n=1, 1, (sinh(Pi)*GAMMA(n-I)*GAMMA(n+I))/(2*Pi)):
seq(simplify(a(n)), n=1..18); # Peter Luschny, Oct 19 2016
MATHEMATICA
a[n_] := Pochhammer[2-I, n-2]*Pochhammer[2+I, n-2]; a[1] = 1; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Dec 21 2012, after Vladeta Jovovic *)
Join[{1}, FoldList[Times, 1, Range[2, 20]^2+1]] (* Harvey P. Dale, Jul 04 2013 *)
Clear[a]; a[1]=1; a[n_]:=a[n]=Sum[i^2*a[i], {i, 1, n-1}]; Table[a[n], {n, 1, 20}] (* Vaclav Kotesovec, Mar 13 2015 *)
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999
EXTENSIONS
More terms from Harvey P. Dale, Jul 04 2013
STATUS
approved