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

1, 1, 2, 3, 5, 8, 14, 23, 39, 65, 109, 182, 305, 510, 854, 1429, 2392, 4003, 6700, 11213, 18767, 31409, 52568, 87980, 147249, 246443, 412461, 690316, 1155350, 1933654, 3236267, 5416387, 9065154, 15171922, 25392535, 42498293, 71127400, 119042590, 199235998, 333451939, 558082864, 934037099

Offset: 0

Author

Joerg Arndt, Sep 30 2012

Keywords

• nonn

Comments

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

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Programs

Maple

a:= proc(n) option remember; local i, s; if n=0 then 1
      else s:=0; for i while i!<=n do s:=s+a(n-i!) od; s fi
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Feb 14 2013

Mathematica

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

PARI

N=66;  x='x+O('x^N);
/* choose upper limit b in following sum such that b! > N */
Vec( 1/( 1 - sum(k=1,7, x^(k!) ) ) )

Formula

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