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A240745 Number of compositions of n having exactly ten fixed points.

%I A240745 #10 Nov 06 2014 09:52:12
%S A240745 1,1,3,7,16,35,76,162,342,715,1484,3049,6266,12788,26017,52773,106791,
%T A240745 215654,434766,875271,1760058,3535850,7097682,14238236,28546852,
%U A240745 57209494,114608933,229529157,459567874,919969090,1841299703,3684822059,7373269689,14752449235
%N A240745 Number of compositions of n having exactly ten fixed points.
%H A240745 Joerg Arndt and Alois P. Heinz, <a href="/A240745/b240745.txt">Table of n, a(n) for n = 55..1000</a>
%F A240745 a(n) ~ c * 2^n, where c = 0.00000000000000004775074360891061857694419107988147903498648930287568336403... . - _Vaclav Kotesovec_, Sep 07 2014
%p A240745 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240745       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 11))
%p A240745     end:
%p A240745 a:= n-> coeff(b(n, 1), x, 10):
%p A240745 seq(a(n), n=55..90);
%t A240745 $RecursionLimit = 500; 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, 11}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 10}]; Table[a[n], {n, 55, 90}] (* _Jean-François Alcover_, Nov 06 2014, after Maple *)
%Y A240745 Column k=10 of A238349 and of A238350.
%K A240745 nonn
%O A240745 55,3
%A A240745 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014