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Join[{0}, Table[n^n 2^(n-1)^2, {n, 10}]] (* Harvey P. Dale, Sep 04 2023 *)
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Delbert L. Johnson, <a href="/A007701/b007701.txt">Table of n, a(n) for n = 0..55</a>
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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].
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a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2).
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.
Additional comments from Michael Somos, Jun 26, 2002
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