A323339 Numerator of the sum of inverse products of parts in all compositions of n.

1, 1, 3, 7, 11, 347, 3289, 1011, 38371, 136553, 4320019, 12528587, 40771123, 29346499543, 129990006917, 1927874590951, 903657004321, 437445829053473, 12456509813711881, 187206004658210129, 1974369484466728177, 1967745662306280217, 21401375717067880189

Offset

0,3

Comments

Numerators of the INVERT transform of reciprocal integers.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..466

Formula

G.f. for fractions: 1 / (1 + log(1 - x)). - Ilya Gutkovskiy, Nov 12 2019

a(n) = numerator( A007840(n)/n! ). - Alois P. Heinz, Jan 04 2024

A323339(n)/A323340(n) ~ exp(n) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Feb 12 2024

Example

1/1, 1/1, 3/2, 7/3, 11/3, 347/60, 3289/360, 1011/70, 38371/1680, 136553/3780, 4320019/75600, 12528587/138600, 40771123/285120, ... = A323339/A323340

Maple

b:= proc(n) option remember;
     `if`(n=0, 1, add(b(n-j)/j, j=1..n))
    end:
a:= n-> numer(b(n)):
seq(a(n), n=0..25);

Mathematica

nmax = 20; Numerator[CoefficientList[Series[1/(1 + Log[1-x]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Feb 12 2024 *)

Crossrefs

Denominators: A323340.

Cf. A000142, A007840, A011782, A088305, A177208, A177209, A322364, A322365, A322380, A322381, A323290, A323291.

Sequence in context: A123259 A116605 A361090 * A057992 A387262 A082600

Adjacent sequences: A323336 A323337 A323338 * A323340 A323341 A323342

Keyword

nonn,frac

Author

Alois P. Heinz, Jan 11 2019

Status

approved