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 A322909 The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 1, ..., n and whose first column consists of 1, n + 1, ..., 2*n - 1. 4
 1, 1, 7, 100, 2840, 129428, 8613997, 791557152, 95921167710, 14818153059968, 2842735387366627, 663020104070865664, 184757202542187563476, 60623405966739216871680, 23135486197103263598936745, 10160292704659539620791062528, 5087671168376607498331875818106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The matrix M(n) differs from that of A306457 in using successive positive integers in place of successive prime numbers. [Modified by Stefano Spezia, Dec 20 2019 at the suggestion of Michel Marcus] The trace of M(n) is A000027(n). The sum of the first row of M(n) is A000217(n). The sum of the first column of M(n) is A005448(n). [Corrected by Stefano Spezia, Dec 19 2019] For n > 1, the sum of the superdiagonal of M(n) is A005843(n). For n > 0, the sum of the (k-1)-th superdiagonal of M(n) is A003991(n,k). - Stefano Spezia, Dec 29 2019 For n > 1 and k > 0, the sum of the k-th subdiagonal of M(n) is A120070(n,k). - Stefano Spezia, Dec 31 2019 LINKS Stefano Spezia, Table of n, a(n) for n = 0..35 Wikipedia, Toeplitz Matrix EXAMPLE For n = 1 the matrix M(1) is    1 with permanent a(1) = 1. For n = 2 the matrix M(2) is    1, 2    3, 1 with permanent a(2) = 7. For n = 3 the matrix M(3) is    1, 2, 3    4, 1, 2    5, 4, 1 with permanent a(3) = 100. MAPLE with(LinearAlgebra): a:= n-> `if`(n=0, 1, Permanent(ToeplitzMatrix([          seq(i, i=2*n-1..n+1, -1), seq(i, i=1..n)]))): seq(a(n), n = 0 .. 15); MATHEMATICA b[n_]:=n; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[1]}, Array[b, n-1, {n+1, 2*n-1}]], Array[b, n]]]]; Array[a, 15, 0] PROG (PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, j, if (j==1, n+i-1)))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; } a(n) = matpermanent(tm(n)); \\ Stefano Spezia, Dec 19 2019 CROSSREFS Cf. A000027, A000217, A003991, A005448, A005843, A120070, A306457, A322908 (determinant of M(n)). Sequence in context: A297151 A052752 A182529 * A165878 A175345 A142358 Adjacent sequences:  A322906 A322907 A322908 * A322910 A322911 A322912 KEYWORD nonn AUTHOR Stefano Spezia, Dec 30 2018 EXTENSIONS a(0) = 1 prepended by Stefano Spezia, Dec 19 2019 STATUS approved

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Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)