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

0,3

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

Formula

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

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 *)

Prog

(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!) ) ) )

Crossrefs

Sequence in context: A078843 A018068 A120400 * A000621 A191317 A218020

Adjacent sequences: A217280 A217281 A217282 * A217284 A217285 A217286

Keyword

nonn

Author

Joerg Arndt, Sep 30 2012

Status

approved