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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)