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Shifts 4 places left under inverse binomial transform.
5

%I #25 Mar 08 2023 03:53:59

%S 1,2,4,8,1,1,1,1,-14,45,-101,189,-331,668,-1932,7206,-27779,101365,

%T -347439,1139851,-3690766,12258863,-43341845,166059261,-682516519,

%U 2930522990,-12823188092,56366526324,-247898684759,1094571175769,-4890163717903,22310147976797

%N Shifts 4 places left under inverse binomial transform.

%H Alois P. Heinz, <a href="/A010743/b010743.txt">Table of n, a(n) for n = 0..740</a>

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

%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 + x^4*A(x/(1 + x))/(1 + x). - _Ilya Gutkovskiy_, Feb 02 2022

%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-4)

%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 - 4];

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

%Y Cf. A010739, A010741, A010745, A010747.

%K sign

%O 0,2

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