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%I M1618 N0632 #38 Aug 09 2020 17:13:16
%S 1,0,0,1,1,1,2,6,17,44,112,304,918,3040,10623,38161,140074,528594,
%T 2068751,8436893,35813251,157448068,713084042,3315414747,15805117878,
%U 77273097114,387692392570,1996280632656,10542604575130,57034787751655,315649657181821
%N Shifts 3 places left under binomial transform.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A000996/b000996.txt">Table of n, a(n) for n = 0..300</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>
%H S. Tauber, <a href="http://www.jstor.org/stable/2308653">On generalizations of the exponential function</a>, Amer. Math. Monthly, 67 (1960), 763-767.
%F G.f. A(x) satisfies: A(x) = 1 + x^3 * A(x/(1 - x)) / (1 - x). - _Ilya Gutkovskiy_, Aug 09 2020
%p a:= proc(n) option remember; local k; if n<=2 then [1,0,0][n+1] else 1+ add(binomial(n-3,k) *a(k), k=3..n-3) fi end: seq(a(n), n=0..29); # _Alois P. Heinz_, Sep 05 2008
%t a[n_] := a[n] = If[n <= 2 , {1, 0, 0}[[n+1]], 1+Sum [Binomial[n-3, k]*a[k], {k, 3, n-3}]]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 24 2014, after _Alois P. Heinz_ *)
%Y Column k=3 of A143983.
%K nonn,eigen
%O 0,7
%A _N. J. A. Sloane_
%E More terms from _Alois P. Heinz_, Sep 05 2008
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