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a(n)=(-1)^n*(-2)^C(n,2)*A001045(n+1).
2

%I #8 Aug 03 2014 14:27:19

%S 1,-1,-6,40,704,-21504,-1409024,178257920,45902462976,-23433341566976,

%T -24030926136672256,49179307930885816320,201512232261203141853184,

%U -1650485975228872480767606784,-27044038098228417485446267797504

%N a(n)=(-1)^n*(-2)^C(n,2)*A001045(n+1).

%C Hankel transform of A186195.

%t f[k_] := (2^(k - 1)) (-1)^(k + 1)

%t t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 22}] (* A186196 signed *)

%t (* _Clark Kimberling_, Dec 30 2011 *)

%K sign,easy

%O 0,3

%A _Paul Barry_, Feb 14 2011