A010739 Shifts 2 places left under inverse binomial transform.

1, 2, 1, 1, -2, 3, -7, 22, -71, 231, -794, 2945, -11679, 48770, -212823, 969221, -4605674, 22802431, -117322423, 625743878, -3452893503, 19684083947, -115787084242, 701935339725, -4380330298815, 28105726916034, -185229395693615, 1252696143653513

Offset: 0

Author

N. J. A. Sloane, Jonas Wallgren

Keywords

• sign
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..650
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A010741, A010743, A010745, A010747.

Programs

Maple

a:= proc(n) option remember; (m-> `if`(m<0, 2^n,
      add(a(m-j)*binomial(m, j)*(-1)^j, j=0..m)))(n-2)
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Feb 02 2022

Mathematica

a[n_] := a[n] = Function[m, If[m<0, 2^n,
   Sum[a[m-j]*Binomial[m, j]*(-1)^j, {j, 0, m}]]][n-2];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 24 2022, after Alois P. Heinz *)

Formula

G.f. A(x) satisfies: A(x) = 1 + 2*x + x^2*A(x/(1 + x))/(1 + x). - Ilya Gutkovskiy, Feb 02 2022