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A105596 a(n) = Sum_{k=0..n} A105595(k)*(-1)^k*A105595(n-k) (interpolated zeros suppressed).

%I A105596 #12 Aug 01 2023 07:37:59
%S A105596 1,5,13,17,25,25,33,21,9,-15,-23,-3,-11,-31,-47,-35,5,-47,-83,-75,
%T A105596 -211,-295,-267,-267,-99,-107,-159,-415,-347,-679,-279,-583,-395,-839,
%U A105596 -1031,-1291,-1139,-1883,-1519,-1643,-855,-1591,-1571,-1851,-1195,-2419,-1923,-2179,-891,-1919,-2535
%N A105596 a(n) = Sum_{k=0..n} A105595(k)*(-1)^k*A105595(n-k) (interpolated zeros suppressed).
%C A105596 Conjecture : a(2n)=1 mod 4 for all n, a(2n+1)=0 for all n.
%p A105596 A105596 := proc(n)
%p A105596     add(A105595(k)*(-1)^k*A105595(2*n-k),k=0..2*n) ;
%p A105596 end proc:
%p A105596 seq(A105596(n),n=0..50) ; # _R. J. Mathar_, Nov 28 2014
%t A105596 A105594[n_, k_] := A105594[n, k] = Sum[Abs[MoebiusMu[ Binomial[n, j]]*Mod[Binomial[j, k], 2]], {j, 0, n}]//Mod[#, 2]&;
%t A105596 A105595[n_] := Sum[A105594[n, k], {k, 0, n}];
%t A105596 a[n_] := Sum[A105595[k]*(-1)^k*A105595[2n - k], {k, 0, 2n}];
%t A105596 Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Aug 01 2023, after _R. J. Mathar_ *)
%Y A105596 Cf. A105594, A105595.
%K A105596 easy,sign
%O A105596 0,2
%A A105596 _Paul Barry_, Apr 14 2005