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A051893 a(n) = Sum_{i=1..n-1} i^2*a(i), a(1) = 1. 3

%I

%S 1,1,5,50,850,22100,817700,40885000,2657525000,217917050000,

%T 22009622050000,2685173890100000,389350214064500000,

%U 66189536390965000000,13039338669020105000000,2946890539198543730000000,757350868574025738610000000,219631751886467464196900000000

%N a(n) = Sum_{i=1..n-1} i^2*a(i), a(1) = 1.

%F a(n) = Product_{i=2..n-1} (i^2+1), for n>2. - _Vladeta Jovovic_, Nov 26 2002

%F From _Vaclav Kotesovec_, Mar 13 2015: (Start)

%F For n > 1, a(n) = A101686(n-1)/2.

%F a(n) ~ (n-1)!^2 * sinh(Pi)/(2*Pi).

%F (End)

%F a(n) = (A003703(n)^2 + A009454(n)^2 + A000007(n-1))/2. - _Vladimir Reshetnikov_, Oct 15 2016

%F a(n) = sinh(Pi)*Gamma(n-I)*Gamma(n+I)/(2*Pi) for n>1. - _Peter Luschny_, Oct 19 2016

%p a := n -> `if`(n=1,1,(sinh(Pi)*GAMMA(n-I)*GAMMA(n+I))/(2*Pi)):

%p seq(simplify(a(n)), n=1..18); # _Peter Luschny_, Oct 19 2016

%t a[n_] := Pochhammer[2-I, n-2]*Pochhammer[2+I, n-2]; a[1] = 1; Table[a[n], {n, 1, 15}] (* _Jean-Fran├žois Alcover_, Dec 21 2012, after _Vladeta Jovovic_ *)

%t Join[{1},FoldList[Times,1,Range[2,20]^2+1]] (* _Harvey P. Dale_, Jul 04 2013 *)

%t 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 *)

%Y Cf. A001710, A101686, A256019, A256020.

%K nice,nonn

%O 1,3

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999

%E More terms from _Harvey P. Dale_, Jul 04 2013

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Last modified April 26 04:11 EDT 2019. Contains 322469 sequences. (Running on oeis4.)