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%I M1485 #33 Jul 16 2021 08:25:32
%S 1,1,1,1,2,5,15,53,213,961,4808,26405,157965,1022573,7122441,53118601,
%T 422362118,3566967917,31887812715,300848966213,2987359924149,
%U 31143724848889,340113005563268,3882897830626949,46254432194746377,573938743829923349,7406289665830324689
%N Shifts 3 places left under exponentiation.
%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="/A007548/b007548.txt">Table of n, a(n) for n = 1..200</a>
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, 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 Ronald Orozco López, <a href="https://www.researchgate.net/publication/350397609_Solution_of_the_Differential_Equation_ykeay_Special_Values_of_Bell_Polynomials_and_ka-Autonomous_Coefficients">Solution of the Differential Equation y^(k)= e^(a*y), Special Values of Bell Polynomials and (k,a)-Autonomous Coefficients</a>, Universidad de los Andes (Colombia 2021).
%F E.g.f. A(x) satisfies differential equation A'''(x)=exp(A(x)), A'(0)=1, A''(0)=1, A'''(0)=1. - _Vladimir Kruchinin_, Nov 19 2011
%p exptr:= proc(p) local g; g:= proc(n) option remember; p(n) +add(binomial(n-1, k-1) *p(k) *g(n-k), k=1..n-1) end: end: b:= exptr(a): a:= n-> `if`(n<=2, 1, b(n-3)): seq(a(n), n=1..30); # _Alois P. Heinz_, Oct 07 2008
%t Exptr[p_] := Module[{g}, g[n_] := g[n] = p[n] + Sum [Binomial[n-1, k-1]*p[k]*g[n-k], {k, 1, n-1}]; g]; b = Exptr [a]; a[n_] := If[n <= 2, 1, b[n-3]]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, May 06 2014, after _Alois P. Heinz_ *)
%K nonn,eigen
%O 1,5
%A _N. J. A. Sloane_.
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