|
%I #24 Mar 02 2022 09:27:02
%S 1,2,4,1,1,1,-6,14,-25,32,6,-250,1222,-4380,13059,-31705,48464,76354,
%T -1159911,7041015,-33400183,135931668,-473704510,1277600695,
%U -1233828142,-16196871172,169736941512,-1156974034428,6577630531262,-32839667759307,142900400342885
%N Shifts 3 places left under inverse binomial transform.
%H Alois P. Heinz, <a href="/A010741/b010741.txt">Table of n, a(n) for n = 0..704</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 + x^3*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-3)
%p end:
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Feb 02 2022
%t a[n_] := a[n] = With[{m = n - 3}, If[m < 0, 2^n,
%t Sum[a[m - j]*Binomial[m, j]*(-1)^j, {j, 0, m}]]];
%t Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Mar 02 2022, after _Alois P. Heinz_ *)
%Y Cf. A010739, A010743, A010745, A010747.
%K sign
%O 0,2
%A _N. J. A. Sloane_, _Jonas Wallgren_
|
