A108176 a(1) = 1, a(n) = (Sum_{k=1..floor(n/2)} 1/a(n + 1 - 2k))*(Product_{k=1..floor(n/2)} a(n + 1 - 2k)).
1, 1, 1, 2, 3, 7, 23, 164, 3786, 620973, 2351006074, 1459911295051236, 3432260322166663402961472, 5010795611887306064313121202903094714708, 17198354961167628388233455836547370709483687001035342768448084064
Offset: 1
Keywords
Crossrefs
Cf. A057438.
Programs
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Maple
a[1]:=1: for n from 2 to 25 do a[n]:=sum(1/a[n+1-2*j],j=1..floor(n/2))*product(a[n+1-2*k],k=1..floor(n/2)) od: seq(a[n],n=1..16); # Emeric Deutsch, Jun 14 2005
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Mathematica
a[1] = 1; a[n_] := a[n] = Sum[1/a[n + 1 - 2k], {k, Floor[n/2]}] Product[ a[n + 1 - 2k], {k, Floor[n/2]}]; Table[ a[n], {n, 15}] (* Robert G. Wilson v, Jun 14 2005 *)
Formula
For n >= 2, a(n+4) = a(n+1)*(a(n+2) - a(n)a(n+1)) + a(n+2)a(n+3).
Extensions
More terms from Robert G. Wilson v and Emeric Deutsch, Jun 14 2005