A010743 Shifts 4 places left under inverse binomial transform.

1, 2, 4, 8, 1, 1, 1, 1, -14, 45, -101, 189, -331, 668, -1932, 7206, -27779, 101365, -347439, 1139851, -3690766, 12258863, -43341845, 166059261, -682516519, 2930522990, -12823188092, 56366526324, -247898684759, 1094571175769, -4890163717903, 22310147976797

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..740

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

Formula

G.f. A(x) satisfies: A(x) = 1 + 2*x + 4*x^2 + 8*x^3 + x^4*A(x/(1 + x))/(1 + x). - Ilya Gutkovskiy, Feb 02 2022

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-4)
    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 - 4];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 08 2023, after Alois P. Heinz *)

Crossrefs

Cf. A010739, A010741, A010745, A010747.

Sequence in context: A339415 A097625 A371133 * A072032 A365814 A023104

Adjacent sequences: A010740 A010741 A010742 * A010744 A010745 A010746

Keyword

sign

Author

N. J. A. Sloane, Jonas Wallgren

Status

approved