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A051893
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a(n) = Sum_{i=1..n-1} i^2*a(i), a(1) = 1.
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3
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1, 1, 5, 50, 850, 22100, 817700, 40885000, 2657525000, 217917050000, 22009622050000, 2685173890100000, 389350214064500000, 66189536390965000000, 13039338669020105000000, 2946890539198543730000000, 757350868574025738610000000, 219631751886467464196900000000
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OFFSET
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1,3
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LINKS
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FORMULA
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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
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MAPLE
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a := n -> `if`(n=1, 1, (sinh(Pi)*GAMMA(n-I)*GAMMA(n+I))/(2*Pi)):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999
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EXTENSIONS
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STATUS
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approved
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