The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A158391 A triangle of matrix polynomials:( dot version) M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]]. 0
 1, 1, -1, 4, -6, 1, 36, -62, 20, -1, 576, -1064, 440, -50, 1, 14400, -27752, 13092, -2068, 105, -1, 518400, -1027872, 526240, -99568, 7476, -196, 1, 25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1, 1625702400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums are: {1, 0, -1, -7, -97, -2224, -75519, -3547169, -219848959, -17364520592, -1701503169057,...}. Example matrix: M(3)={{14, 5, 1}, {5, 5, 1}, {1, 1, 1}} LINKS FORMULA M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]]; out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x) EXAMPLE {1}, {1, -1}, {4, -6, 1}, {36, -62, 20, -1}, {576, -1064, 440, -50, 1}, {14400, -27752, 13092, -2068, 105, -1}, {518400, -1027872, 526240, -99568, 7476, -196, 1}, {25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1}, {1625702400, -3340564992, 1883221312, -432454176, 46632432, -2444400, 59004, -540, 1}, {131681894400, -273837169152, 159196654656, -38743828352, 4614308240, -285357704, 9115756, -139260, 825, -1}, {13168189440000, -27647080704000, 16465714101504, -4189435579520, 537035259392, -37331932704, 1435658576, -29713112, 302016, -1210, 1} MATHEMATICA Clear[M, T, d, a, x, a0]; M[d_] :=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]]; a0 = Table[M[d], {d, 1, 10}]; Table[Det[M[d]], {d, 1, 10}]; Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}]; Flatten[a] Join[{1}, Table[Apply[Plus, CoefficientList[ Expand[CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]; CROSSREFS Sequence in context: A230256 A193293 A258220 * A016491 A160327 A124259 Adjacent sequences:  A158388 A158389 A158390 * A158392 A158393 A158394 KEYWORD sign,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Mar 17 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 21 03:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)