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A240744 Number of compositions of n having exactly nine fixed points.

%I A240744 #11 Nov 06 2014 09:52:18
%S A240744 1,1,3,7,16,35,76,162,342,715,1474,3049,6245,12746,25922,52571,106353,
%T A240744 214731,432827,871240,1751725,3518787,7062725,14167004,28402284,
%U A240744 56916681,114017164,228335406,457163368,915131854,1831578490,3665302380,7334102844,14673905376
%N A240744 Number of compositions of n having exactly nine fixed points.
%H A240744 Joerg Arndt and Alois P. Heinz, <a href="/A240744/b240744.txt">Table of n, a(n) for n = 45..1000</a>
%F A240744 a(n) ~ c * 2^n, where c = 0.00000000000004863374631933235641619389991611011374568106537836728124272498... . - _Vaclav Kotesovec_, Sep 07 2014
%p A240744 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240744       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 10))
%p A240744     end:
%p A240744 a:= n-> coeff(b(n, 1), x, 9):
%p A240744 seq(a(n), n=45..80);
%t A240744 b[n_, i_] := b[n, i] = If[n == 0, 1, Series[Sum[b[n - j, i + 1]*If[i == j, x, 1], {j, 1, n}], {x, 0, 10}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 9}]; Table[a[n], {n, 45, 80}] (* _Jean-François Alcover_, Nov 06 2014, after Maple *)
%Y A240744 Column k=9 of A238349 and of A238350.
%K A240744 nonn
%O A240744 45,3
%A A240744 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014