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URL: https://oeis.org/A217283

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A217283
Expansion of 1/(1 -x -x^2 -x^6 -x^24 - ... -x^(k!) - ... ).
1
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, Sep 30 2012
STATUS
approved