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A323339 Numerator of the sum of inverse products of parts in all compositions of n. 9
1, 1, 3, 7, 11, 347, 3289, 1011, 38371, 136553, 4320019, 12528587, 40771123, 29346499543, 129990006917, 1927874590951, 903657004321, 437445829053473, 12456509813711881, 187206004658210129, 1974369484466728177, 1967745662306280217, 21401375717067880189 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Numerators of the INVERT transform of reciprocal integers.
LINKS
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.
Sequence in context: A123259 A116605 A361090 * A057992 A082600 A355314
KEYWORD
nonn,frac
AUTHOR
Alois P. Heinz, Jan 11 2019
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)