Search: id:A101686
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%I A101686
%S A101686 1,2,10,100,1700,44200,1635400,81770000,5315050000,435834100000,
%T A101686 44019244100000,5370347780200000,778700428129000000,
%U A101686 132379072781930000000,26078677338040210000000
%N A101686 Sum of all coefficients in Prod[k=0..n, x+k^2 ].
%C A101686 Row sums of triangle of central factorial numbers (A008955).
%C A101686 "HANOWA" is a matrix whose eigenvalues lie on a vertical line. It is 
               an N X N matrix with 2 X 2 blocks with identity matrices in the upper 
               left and lower right blocks and diagonal matrices containing the 
               first N integers in the upper right and lower left blocks. In Matlab, 
               the following code generates the sequence... for n=0:2:TERMS*2 det(gallery('hanowa',
               n)) end - Paul M. Payton (paul.payton(AT)lmco.com), Mar 31 2005
%C A101686 Cilleruelo shows that a(n) is a square only for n =0 and 3. - Charles 
               R Greathouse IV, Aug 27 2008
%D A101686 Javier Cilleruelo, "Squares in (1^2+1)...(n^2+1)", Journal of Number 
               Theory 128:8 (2008), pp. 2488-2491.
%H A101686 Charles R Greathouse IV, <a href="http://math.crg4.com/">Home Page</a> 
               [in lieu of email address]
%p A101686 with (combinat):a:=n->mul(fibonacci(3,i), i=0..n):seq(a(n), n=0..14); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2008
%o A101686 (PARI) a(n)=prod(k=1,n,k^2+1) - Charles R Greathouse IV, Aug 27 2008
%Y A101686 Equals 2 * A051893(n-1), n>0.
%Y A101686 Sequence in context: A098279 A099826 A063959 this_sequence A074109 A036336 
               A070842
%Y A101686 Adjacent sequences: A101683 A101684 A101685 this_sequence A101687 A101688 
               A101689
%K A101686 nonn
%O A101686 0,2
%A A101686 Ralf Stephan, Dec 13 2004
%E A101686 More terms from Charles R Greathouse IV, Aug 27 2008

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