A130708 Number of compositions of n such that every part divides the largest part.
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
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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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
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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 *)
Formula
G.f.: 1 + Sum_{n>0} x^n/((1-Sum_{d divides n} x^d)*(1-Sum_{d divides n,d
Extensions
More terms from R. J. Mathar, Oct 28 2007