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A240740 Number of compositions of n having exactly five fixed points.

%I A240740 #11 Nov 07 2014 03:44:27
%S A240740 1,1,3,7,16,35,70,155,321,665,1368,2802,5711,11623,23526,47567,95967,
%T A240740 193316,388893,781519,1569154,3148292,6313052,12652917,25349663,
%U A240740 50770869,101658425,203506976,407323589,815151106,1631122032,3263576647,6529319168,13062156519
%N A240740 Number of compositions of n having exactly five fixed points.
%H A240740 Joerg Arndt and Alois P. Heinz, <a href="/A240740/b240740.txt">Table of n, a(n) for n = 15..1000</a>
%F A240740 a(n) ~ c * 2^n, where c = 0.00004645976701216392005148703795279235922588728788878226802174676992574918... . - _Vaclav Kotesovec_, Sep 07 2014
%e A240740 a(17) = 3: 123416, 123452, 1234511.
%e A240740 a(18) = 7: 123156, 123426, 123453, 1234161, 1234512, 1234521, 12345111.
%e A240740 a(19) = 16: 121456, 123256, 123436, 123454, 1231561, 1234117, 1234162, 1234261, 1234513, 1234522, 1234531, 12341611, 12345112, 12345121, 12345211, 123451111.
%p A240740 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240740       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 6))
%p A240740     end:
%p A240740 a:= n-> coeff(b(n, 1), x, 5):
%p A240740 seq(a(n), n=15..50);
%t A240740 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, 6}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 5}]; Table[a[n], {n, 15, 50}] (* _Jean-François Alcover_, Nov 07 2014, after Maple *)
%Y A240740 Column k=5 of A238349 and of A238350.
%K A240740 nonn
%O A240740 15,3
%A A240740 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014