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 A177147 a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive triangular numbers. 1
 1, -8, 190, -8880, 683375, -78206688, 12452171844, -2631354777600, 712425472573815, -240455417915625000, 98981390235327670642, -48810267466347374088192, 28406348214047496113497895, -19264981823338548859573191040, 15061032335471422549306640625000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n). EXAMPLE a(4) = determinant of 4 X 4 matrix | 1,  3,  6, 10| |10,  1,  3,  6| | 6, 10,  1,  3| | 3,  6, 10,  1| = -8880. MATHEMATICA tri[n_] := n (n + 1)/2; f[n_] := Det[ Table[ RotateLeft[ tri@ Range@ n, -j], {j, 0, n - 1}]]; Array[f, 15] (* or *) f[n_] := (-1)^n*n^(n - 2)(n + 1)(n + 2)((n + 1)^n - (n + 3)^n)/(3*2^(n + 1)); Array[f, 15]  (* Robert G. Wilson v, Aug 31 2014 *) PROG (PARI) A177147(n)={ (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n) ; } { for(n=1, 20, print1(A177147(n)", ") ; ) ; } \\ R. J. Mathar, May 28 2010 CROSSREFS Cf. A118705. Sequence in context: A244438 A272529 A198282 * A251669 A158654 A275995 Adjacent sequences:  A177144 A177145 A177146 * A177148 A177149 A177150 KEYWORD easy,sign AUTHOR Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010 EXTENSIONS More terms from R. J. Mathar, May 28 2010 Two more terms from Robert G. Wilson v, Aug 31 2014 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)