A038074 Shifts left and changes sign under Weigh transform.

1, -1, 1, 0, -2, 2, 2, -6, 4, 8, -23, 12, 43, -95, 28, 223, -420, 6, 1194, -1860, -597, 6405, -8235, -6221, 34441, -35405, -48444, 184208, -143567, -337144, 976873, -512835, -2207538, 5112758, -1290534, -13896631, 26279179, 1478847, -84969584, 131756101

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> `if`(n=1, 1, -b((n-1)$2)):
seq(a(n), n=1..60);  # Alois P. Heinz, May 20 2013

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
     Sum[Binomial[a[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]];
a[n_] := If[n == 1, 1, -b[n - 1, n - 1]];
Array[a, 60] (* Jean-François Alcover, Mar 01 2021, after Alois P. Heinz *)

Crossrefs

Cf. A038073.

Sequence in context: A131904 A278264 A232114 * A059885 A259689 A300413

Adjacent sequences: A038071 A038072 A038073 * A038075 A038076 A038077

Keyword

sign,eigen

Author

Christian G. Bower, Jan 04 1999

Status

approved