A010741 Shifts 3 places left under inverse binomial transform.

1, 2, 4, 1, 1, 1, -6, 14, -25, 32, 6, -250, 1222, -4380, 13059, -31705, 48464, 76354, -1159911, 7041015, -33400183, 135931668, -473704510, 1277600695, -1233828142, -16196871172, 169736941512, -1156974034428, 6577630531262, -32839667759307, 142900400342885

Offset: 0

Author

N. J. A. Sloane, Jonas Wallgren

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..704
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.
• 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, 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-3)
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Feb 02 2022

Mathematica

a[n_] := a[n] = With[{m = n - 3}, If[m < 0, 2^n,
     Sum[a[m - j]*Binomial[m, j]*(-1)^j, {j, 0, m}]]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 02 2022, after Alois P. Heinz *)

Formula

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