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Revision History for A007701

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Showing entries 1-10 | older changes
a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2).
(history; published version)
#26 by Harvey P. Dale at Mon Sep 04 12:53:29 EDT 2023
STATUS

editing

approved

#25 by Harvey P. Dale at Mon Sep 04 12:53:26 EDT 2023
MATHEMATICA

Join[{0}, Table[n^n 2^(n-1)^2, {n, 10}]] (* Harvey P. Dale, Sep 04 2023 *)

STATUS

approved

editing

#24 by Michael De Vlieger at Sun Mar 26 10:29:37 EDT 2023
STATUS

reviewed

approved

#23 by Michel Marcus at Sun Mar 26 02:07:39 EDT 2023
STATUS

proposed

reviewed

#22 by Delbert L. Johnson at Sat Mar 25 21:03:09 EDT 2023
STATUS

editing

proposed

#21 by Delbert L. Johnson at Sat Mar 25 21:03:02 EDT 2023
LINKS

Delbert L. Johnson, <a href="/A007701/b007701.txt">Table of n, a(n) for n = 0..55</a>

STATUS

approved

editing

#20 by N. J. A. Sloane at Tue May 08 15:11:54 EDT 2018
LINKS

M. Abramowitz and I. A. Stegun, eds., <a href="http://appswww.nrbookconvertit.com/abramowitz_and_stegunGo/ConvertIt/Reference/indexAMS55.htmlASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Discussion
Tue May 08
15:11
OEIS Server: https://oeis.org/edit/global/2759
#19 by Bruno Berselli at Tue Jan 09 03:01:14 EST 2018
STATUS

proposed

approved

#18 by Jon E. Schoenfield at Mon Jan 08 22:14:03 EST 2018
STATUS

editing

proposed

#17 by Jon E. Schoenfield at Mon Jan 08 22:13:14 EST 2018
NAME

a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2).

FORMULA

a(n) = (n^n)*2^((n-1)^2), n >= 1, a(0):=0.

a(n) = ((2^((n-1)^2))*Det(Vn(xn[1],..,.,xn[n])))^2, n >= 1, with the determinant of the Vandermonde matrix Vn with elements (Vn)i,j:= xn[i]^j, i=1..n,j=0..n-1 and xn[i]:=cos((2*i-1)*Pi/(2*n)), i=1,..,n, are the zeros of the Chebyshev T(n,x) polynomials.

a(n) = ((-1)^(n*(n-1)/2))*(2^((n-1)*(n-2))) * productProduct_{i=1..n} (diff(d/dx)T(n,x),x)|_{x=xn[i]},i=1..n), n > 0, with the zeros xn[i], i=1..n, given above.

AUTHOR
EXTENSIONS

Additional comments from Michael Somos, Jun 26, 2002

STATUS

approved

editing