|
|
A130708
|
|
Number of compositions of n such that every part divides the largest part.
|
|
1
|
|
|
1, 1, 2, 4, 8, 14, 26, 45, 79, 137, 241, 423, 754, 1343, 2410, 4344, 7870, 14305, 26103, 47763, 87649, 161229, 297251, 549108, 1016243, 1883898, 3497761, 6503420, 12107958, 22570221, 42121298, 78692765, 147165225, 275476533, 516115940
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1 + Sum_{n>0} x^n/((1-Sum_{d divides n} x^d)*(1-Sum_{d divides n,d<n} x^d)).
|
|
MAPLE
|
A130708 := proc(n) local gf, den1, den2, i, d ; gf := 1 ; for i from 1 to n do den1 := 1 ; den2 := 1 ; for d in numtheory[divisors](i) do den1 := den1-x^d ; if d < i then den2 := den2-x^d ; fi ; od ; gf := taylor(gf+x^i/den1/den2, x=0, n+1) ; od: coeftayl(gf, x=0, n) ; end: seq(A130708(n), n=0..40) ; # R. J. Mathar, Oct 28 2007
|
|
MATHEMATICA
|
m = 35;
1 + Sum[x^n/((1 - Sum[x^d, {d, Divisors[n]}]) (1 - Sum[Boole[d < n] x^d, {d, Divisors[n]}])), {n, 1, m}] + O[x]^m // CoefficientList[#, x]& (* Jean-François Alcover, May 22 2020 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|