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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322908 The determinant 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, -5, 38, -386, 4928, -75927, 1371808, -28452356, 666445568, -17402398505, 501297595904, -15792876550662, 540190822408192, -19937252888438459, 789770307546718208, -33422580292067020808, 1504926927960887066624, -71839548181524098808909, 3624029163661165580910592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The matrix M(n) differs from that of A318173 in using successive positive integers in place of successive prime numbers. The trace of the matrix M(n) is A000027(n). The sum of the first row of the matrix M(n) is A000217(n). The sum of the first column of the matrix M(n) is A005448(n). [Corrected by Stefano Spezia, Dec 11 2019] For n > 1, the sum of the superdiagonal of the matrix M(n) is A005843(n). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..300 Wikipedia, Toeplitz Matrix FORMULA a(n) ~ -(-1)^n * (3*exp(1) - exp(-1)) * n^n / 4. - Vaclav Kotesovec, Jan 05 2019 EXAMPLE For n = 1 the matrix M(1) is    1 with determinant Det(M(1)) = 1. For n = 2 the matrix M(2) is    1, 2    3, 1 with Det(M(2)) = -5. For n = 3 the matrix M(3) is    1, 2, 3    4, 1, 2    5, 4, 1 with Det(M(3)) = 38. MAPLE a:= proc(n) uses LinearAlgebra; Determinant(ToeplitzMatrix([seq(i, i=2*n-1..n+1, -1), seq(i, i=1..n)])) end proc: map(a, [\$1..20]); MATHEMATICA b[n_]:=n; a[n_]:=Det[ToeplitzMatrix[Join[{b[1]}, Array[b, n-1, {n+1, 2*n-1}]], Array[b, n]]]; Array[a, 20] 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) = matdet(tm(n)); \\ Michel Marcus, Nov 11 2020 CROSSREFS Cf. A000027, A000217, A005448, A005843, A318173. Cf. A322909 (permanent of matrix M(n)). Sequence in context: A243690 A335530 A308877 * A098937 A190314 A217701 Adjacent sequences:  A322905 A322906 A322907 * A322909 A322910 A322911 KEYWORD sign AUTHOR Stefano Spezia, Dec 30 2018 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 November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)