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A051165 Sequence is defined by property that binomial transform of (a0,a1,a2,a3,...) = (a0,a0,a1,a1,a2,a2,a3,a3,...).

%I A051165 #13 Jun 04 2018 03:11:55
%S A051165 1,0,-1,2,-4,8,-12,8,15,-56,81,-26,-130,208,306,-2060,4796,-5120,
%T A051165 -6140,43320,-113768,182720,-111768,-395696,1725172,-3922016,5614348,
%U A051165 -2289912,-14957416,56700032,-121684568,164735504,-47657969,-491084768,1740799985,-3598600386,4619098604
%N A051165 Sequence is defined by property that binomial transform of (a0,a1,a2,a3,...) = (a0,a0,a1,a1,a2,a2,a3,a3,...).
%H A051165 Alois P. Heinz, <a href="/A051165/b051165.txt">Table of n, a(n) for n = 0..1000</a>
%H A051165 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A051165 a:= proc(n) option remember; add(`if`(k<2, 1,
%p A051165       a(iquo(k, 2)))*(-1)^(n-k)*binomial(n, k), k=0..n)
%p A051165     end:
%p A051165 seq(a(n), n=0..45);  # _Alois P. Heinz_, Jul 08 2015
%t A051165 a[n_] := a[n] = Sum[If[k<2, 1, a[Quotient[k, 2]]]*(-1)^(n-k)*Binomial[n, k], {k, 0, n}];
%t A051165 Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, Jun 04 2018, from Maple *)
%Y A051165 Cf. A051163, A051164, A051166.
%K A051165 easy,sign,eigen
%O A051165 0,4
%A A051165 _Jonas Wallgren_
%E A051165 More terms from _Vladeta Jovovic_, Jul 26 2002