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

1, 0, -1, 2, -4, 8, -12, 8, 15, -56, 81, -26, -130, 208, 306, -2060, 4796, -5120, -6140, 43320, -113768, 182720, -111768, -395696, 1725172, -3922016, 5614348, -2289912, -14957416, 56700032, -121684568, 164735504, -47657969, -491084768, 1740799985, -3598600386, 4619098604

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Maple

a:= proc(n) option remember; add(`if`(k<2, 1,
      a(iquo(k, 2)))*(-1)^(n-k)*binomial(n, k), k=0..n)
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Jul 08 2015

Mathematica

a[n_] := a[n] = Sum[If[k<2, 1, a[Quotient[k, 2]]]*(-1)^(n-k)*Binomial[n, k], {k, 0, n}];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Jun 04 2018, from Maple *)

Crossrefs

Cf. A051163, A051164, A051166.

Sequence in context: A349228 A337181 A357806 * A009664 A009507 A064657

Adjacent sequences: A051162 A051163 A051164 * A051166 A051167 A051168

Keyword

easy,sign,eigen

Author

Jonas Wallgren

Extensions

More terms from Vladeta Jovovic, Jul 26 2002

Status

approved