A217283 - OEIS

%I #20 Nov 11 2018 23:10:46

%S 1,1,2,3,5,8,14,23,39,65,109,182,305,510,854,1429,2392,4003,6700,

%T 11213,18767,31409,52568,87980,147249,246443,412461,690316,1155350,

%U 1933654,3236267,5416387,9065154,15171922,25392535,42498293,71127400,119042590,199235998,333451939,558082864,934037099

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

%C Number of compositions of n into parts 1, 2, 6, 24, ..., k!, ...

%C The first terms are the same as for A120400, but the two sequences are different.

%H Alois P. Heinz, <a href="/A217283/b217283.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^k! ).

%p a:= proc(n) option remember; local i, s; if n=0 then 1

%p       else s:=0; for i while i!<=n do s:=s+a(n-i!) od; s fi

%p     end:

%p seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 14 2013

%t nn=41;CoefficientList[Series[1/(1-Sum[x^(i!),{i,1,10}]),{x,0,nn}],x] (* _Geoffrey Critzer_, Sep 29 2013 *)

%o (PARI)

%o N=66;  x='x+O('x^N);

%o /* choose upper limit b in following sum such that b! > N */

%o Vec( 1/( 1 - sum(k=1,7, x^(k!) ) ) )

%K nonn

%O 0,3

%A _Joerg Arndt_, Sep 30 2012