|
|
A322364
|
|
Numerator of the sum of inverse products of parts in all partitions of n.
|
|
8
|
|
|
1, 1, 3, 11, 7, 27, 581, 4583, 2327, 69761, 775643, 147941, 30601201, 30679433, 10928023, 6516099439, 445868889691, 298288331489, 7327135996801, 1029216937671847, 14361631943741, 837902013393451, 2766939485246012129, 274082602410356881, 835547516381094139939
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
1/1, 1/1, 3/2, 11/6, 7/3, 27/10, 581/180, 4583/1260, 2327/560, 69761/15120, 775643/151200, 147941/26400, 30601201/4989600, 30679433/4633200 ... = A322364/A322365
|
|
MAPLE
|
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
b(n, i-1) +b(n-i, min(i, n-i))/i)
end:
a:= n-> numer(b(n$2)):
seq(a(n), n=0..30);
|
|
MATHEMATICA
|
b[n_, i_] := b[n, i] = If[n==0||i==1, 1, b[n, i-1] + b[n-i, Min[i, n-i]]/i];
a[n_] := Numerator[b[n, n]];
|
|
PROG
|
(PARI) a(n) = {my(s=0); forpart(p=n, s += 1/vecprod(Vec(p))); numerator(s); } \\ Michel Marcus, Apr 29 2020
|
|
CROSSREFS
|
Cf. A000041, A006906, A080130, A177208, A177209, A322380, A322381, A323290, A323291, A323339, A323340.
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|