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A143126
a(n) = (1-2n)*2^n.
1
1, -2, -12, -40, -112, -288, -704, -1664, -3840, -8704, -19456, -43008, -94208, -204800, -442368, -950272, -2031616, -4325376, -9175040, -19398656, -40894464, -85983232, -180355072, -377487360, -788529152, -1644167168, -3422552064, -7113539584, -14763950080
OFFSET
0,2
COMMENTS
Hankel transform of abs(A002420) (which is 2*0^n - binomial(2n,n)/(2n-1)).
FORMULA
G.f.: (1-6x)/(1-2x)^2;
a(n) = Sum_{k=0..n} A121314(n,k)*(-1)^k*2^(3n-2k). - Philippe Deléham, Oct 31 2008
From Amiram Eldar, Oct 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 1 - arcsinh(1)/sqrt(2).
Sum_{n>=0} (-1)^n/a(n) = 1 + arctan(1/sqrt(2))/sqrt(2). (End)
MATHEMATICA
a[n_] := (1-2n)*2^n; Array[a, 40, 0] (* Amiram Eldar, Oct 01 2022 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jul 26 2008
STATUS
approved