A010747 - OEIS

%I #33 Mar 08 2023 06:27:09

%S 1,2,4,8,16,32,1,1,1,1,1,1,-62,315,-1002,2505,-5377,10373,-18544,

%T 32086,-60468,154687,-567986,2422043,-10225382,40740231,-152497274,

%U 539809668,-1822828757,5928049329,-18782176673,58918636670,-187382010256,623524250516

%N Shifts 6 places left under inverse binomial transform.

%H Alois P. Heinz, <a href="/A010747/b010747.txt">Table of n, a(n) for n = 0..802</a>

%H M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F G.f. A(x) satisfies: A(x) = 1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4 + 32*x^5 + x^6*A(x/(1 + x))/(1 + x). - _Ilya Gutkovskiy_, Feb 02 2022

%F a(n) = 2^n for n<6; otherwise a(n) = Sum_{j=0..n-6} a(n-6-j)*binomial(n-6,j)*(-1)^j. - _Michel Marcus_, Mar 08 2023

%p a:= proc(n) option remember; (m-> `if`(m<0, 2^n,

%p       add(a(m-j)*binomial(m, j)*(-1)^j, j=0..m)))(n-6)

%p     end:

%p seq(a(n), n=0..35);  # _Alois P. Heinz_, Feb 02 2022

%t a[n_] := a[n] = Function[m, If[m < 0, 2^n, Sum[a[m - j]* Binomial[m, j]*(-1)^j, {j, 0, m}]]][n - 6];

%t Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Mar 08 2023, after _Alois P. Heinz_ *)

%Y Cf. A010739, A010741, A010743, A010745.

%K sign,eigen

%O 0,2

%A _N. J. A. Sloane_, _Jonas Wallgren_