A010745 Shifts 5 places left under inverse binomial transform.

1, 2, 4, 8, 16, 1, 1, 1, 1, 1, -30, 124, -336, 734, -1401, 2404, -3485, 2212, 14630, -105408, 497131, -1995782, 7265342, -24576128, 77966104, -231218343, 626012198, -1430352680, 1894959964, 6114950887, -73791743479, 472896657475, -2523776826105, 12272646042530

Offset: 0

Author

N. J. A. Sloane, Jonas Wallgren

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..775
• 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 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. A010739, A010741, A010743, 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-5)
    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-5]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)

Formula

G.f. A(x) satisfies: A(x) = 1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4 + x^5*A(x/(1 + x))/(1 + x). - Ilya Gutkovskiy, Feb 02 2022