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 A208057 Triangle by rows, generated from the odd integers and related to A000165. 3
 1, 1, 1, 4, 3, 1, 24, 18, 5, 1, 192, 144, 40, 7, 1, 1920, 1440, 400, 70, 9, 1, 23040, 17280, 4800, 840, 108, 11, 1, 322560, 241920, 67200, 11760, 1512, 154, 13, 1, 5160960, 3870720, 1075200, 188160, 24192, 2464, 208, 15, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums = A000165, the double factorial numbers: (1, 2, 8, 48, 384,...). Left border = A002866 and the eigensequence of the odd integers prefaced with a 1. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA Eigentriangle of triangle A158405 (odd integers in every row: (1, 3, 5,...); the inverse of: 1; -1, 1; -1, -3, 1; -1, -3, -5, 1; -1, -3, -5, -7, 1; ... EXAMPLE First few rows of the triangle = 1; 1, 1; 4, 3, 1; 24, 18, 5, 1; 192, 144, 40, 7, 1; 1920, 1440, 400, 70, 9, 1; 23040, 17280, 4800, 840, 108, 11, 1; 322560, 241920, 67200, 11760, 1512, 154, 13, 1; ... MAPLE T:= proc(n) option remember; local M; M:= (Matrix(n+1, (i, j)-> `if`(i=j, 1, `if`(i>j, -2*j+1, 0)))^(-1)); seq(M[n+1, k], k=1..n+1) end: seq(T(n), n=0..10); # Alois P. Heinz, Feb 27 2012 MATHEMATICA T[n_] := T[n] = Module[{M}, M = Table[If[i == j, 1, If[i>j, -2*j+1, 0]], {i, 1, n+1 }, {j, 1, n+1}] // Inverse; M[[n+1]]]; Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *) CROSSREFS Cf. A000165, A002866, A158405. Sequence in context: A189507 A348436 A350528 * A298673 A245732 A039621 Adjacent sequences: A208054 A208055 A208056 * A208058 A208059 A208060 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Feb 22 2012 EXTENSIONS Typo in term 17 corrected by Alois P. Heinz, Dec 06 2012 STATUS approved

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Last modified June 5 22:25 EDT 2023. Contains 363138 sequences. (Running on oeis4.)