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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Cf. A100346, A018818, A083710, A097986, A117086.

Sequence in context: A036609 A027557 A120545 * A228805 A317884 A378196

Adjacent sequences: A130705 A130706 A130707 * A130709 A130710 A130711

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 01 2007

Extensions

More terms from R. J. Mathar, Oct 28 2007

Status

approved