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

1, 5, 13, 17, 25, 25, 33, 21, 9, -15, -23, -3, -11, -31, -47, -35, 5, -47, -83, -75, -211, -295, -267, -267, -99, -107, -159, -415, -347, -679, -279, -583, -395, -839, -1031, -1291, -1139, -1883, -1519, -1643, -855, -1591, -1571, -1851, -1195, -2419, -1923, -2179, -891, -1919, -2535

Offset: 0

Author

Paul Barry, Apr 14 2005

Keywords

• easy
• sign

Comments

Conjecture : a(2n)=1 mod 4 for all n, a(2n+1)=0 for all n.

Crossrefs

Cf. A105594, A105595.

Programs

Maple

A105596 := proc(n)
    add(A105595(k)*(-1)^k*A105595(2*n-k),k=0..2*n) ;
end proc:
seq(A105596(n),n=0..50) ; # R. J. Mathar, Nov 28 2014

Mathematica

A105594[n_, k_] := A105594[n, k] = Sum[Abs[MoebiusMu[ Binomial[n, j]]*Mod[Binomial[j, k], 2]], {j, 0, n}]//Mod[#, 2]&;
A105595[n_] := Sum[A105594[n, k], {k, 0, n}];
a[n_] := Sum[A105595[k]*(-1)^k*A105595[2n - k], {k, 0, 2n}];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)