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Search: id:A101686
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| A101686 |
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Sum of all coefficients in Prod[k=0..n, x+k^2 ]. |
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3
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| 1, 2, 10, 100, 1700, 44200, 1635400, 81770000, 5315050000, 435834100000, 44019244100000, 5370347780200000, 778700428129000000, 132379072781930000000, 26078677338040210000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums of triangle of central factorial numbers (A008955).
"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
Cilleruelo shows that a(n) is a square only for n =0 and 3. - Charles R Greathouse IV, Aug 27 2008
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REFERENCES
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Javier Cilleruelo, "Squares in (1^2+1)...(n^2+1)", Journal of Number Theory 128:8 (2008), pp. 2488-2491.
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LINKS
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Charles R Greathouse IV, Home Page [in lieu of email address]
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MAPLE
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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
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PROGRAM
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(PARI) a(n)=prod(k=1, n, k^2+1) - Charles R Greathouse IV, Aug 27 2008
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CROSSREFS
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Equals 2 * A051893(n-1), n>0.
Sequence in context: A098279 A099826 A063959 this_sequence A074109 A036336 A070842
Adjacent sequences: A101683 A101684 A101685 this_sequence A101687 A101688 A101689
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Dec 13 2004
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EXTENSIONS
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More terms from Charles R Greathouse IV, Aug 27 2008
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