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A217283 Expansion of 1/(1 -x -x^2 -x^6 -x^24 - ... -x^(k!) - ... ).

%I A217283 #20 Nov 11 2018 23:10:46
%S A217283 1,1,2,3,5,8,14,23,39,65,109,182,305,510,854,1429,2392,4003,6700,
%T A217283 11213,18767,31409,52568,87980,147249,246443,412461,690316,1155350,
%U A217283 1933654,3236267,5416387,9065154,15171922,25392535,42498293,71127400,119042590,199235998,333451939,558082864,934037099
%N A217283 Expansion of 1/(1 -x -x^2 -x^6 -x^24 - ... -x^(k!) - ... ).
%C A217283 Number of compositions of n into parts 1, 2, 6, 24, ..., k!, ...
%C A217283 The first terms are the same as for A120400, but the two sequences are different.
%H A217283 Alois P. Heinz, <a href="/A217283/b217283.txt">Table of n, a(n) for n = 0..1000</a>
%F A217283 G.f.: 1/(1 - Sum_{k>=1} x^k! ).
%p A217283 a:= proc(n) option remember; local i, s; if n=0 then 1
%p A217283       else s:=0; for i while i!<=n do s:=s+a(n-i!) od; s fi
%p A217283     end:
%p A217283 seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 14 2013
%t A217283 nn=41;CoefficientList[Series[1/(1-Sum[x^(i!),{i,1,10}]),{x,0,nn}],x] (* _Geoffrey Critzer_, Sep 29 2013 *)
%o A217283 (PARI)
%o A217283 N=66;  x='x+O('x^N);
%o A217283 /* choose upper limit b in following sum such that b! > N */
%o A217283 Vec( 1/( 1 - sum(k=1,7, x^(k!) ) ) )
%K A217283 nonn
%O A217283 0,3
%A A217283 _Joerg Arndt_, Sep 30 2012