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A010739
Shifts 2 places left under inverse binomial transform.
10
1, 2, 1, 1, -2, 3, -7, 22, -71, 231, -794, 2945, -11679, 48770, -212823, 969221, -4605674, 22802431, -117322423, 625743878, -3452893503, 19684083947, -115787084242, 701935339725, -4380330298815, 28105726916034, -185229395693615, 1252696143653513
OFFSET
0,2
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; 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
FORMULA
G.f. A(x) satisfies: A(x) = 1 + 2*x + x^2*A(x/(1 + x))/(1 + x). - Ilya Gutkovskiy, Feb 02 2022
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-2)
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-2];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 24 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
sign,eigen
STATUS
approved