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%I #39 Sep 08 2022 08:44:33
%S 1,3,15,75,375,1875,9375,46875,234375,1171875,5859375,29296875,
%T 146484375,732421875,3662109375,18310546875,91552734375,457763671875,
%U 2288818359375,11444091796875,57220458984375
%N Expand (1-2*x)/(1-5*x).
%C a(n) is the number of generalized compositions of n when there are 3*2^(i-1) different types of i, (i=1,2,...). - _Milan Janjic_, Sep 24 2010
%C INVERTi transform of A180034: (1, 4, 22, 124, 700, ...). - _Gary W. Adamson_, Aug 10 2016
%H G. C. Greubel, <a href="/A005053/b005053.txt">Table of n, a(n) for n = 0..1000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=883">Encyclopedia of Combinatorial Structures 883</a>
%F Binomial transform of A122117. - _Philippe Deléham_, Oct 19 2006
%F a(0) = 1, a(n) = 3*5^(n-1) for n >= 1. - _Philippe Deléham_, Oct 19 2006
%F E.g.f.: (2 + 3*exp(5*x))/5. - _Ilya Gutkovskiy_, Aug 11 2016
%t CoefficientList[Series[(1-2x)/(1-5x),{x,0,30}],x] (* or *) Join[{1}, NestList[5#&,3,29]] (* _Harvey P. Dale_, Apr 25 2011 *)
%o (Magma) [ n eq 0 select 1 else 3*5^(n-1): n in [0..20] ]; // _Klaus Brockhaus_, Apr 04 2010
%o (PARI) x='x+O('x^50); Vec((1-2*x)/(1-5*x)) \\ _G. C. Greubel_, Sep 15 2017
%Y Cf. A180034.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E Wrong formula deleted by _Klaus Brockhaus_, Apr 04 2010
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