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A322364 Numerator of the sum of inverse products of parts in all partitions of n. 8

%I

%S 1,1,3,11,7,27,581,4583,2327,69761,775643,147941,30601201,30679433,

%T 10928023,6516099439,445868889691,298288331489,7327135996801,

%U 1029216937671847,14361631943741,837902013393451,2766939485246012129,274082602410356881,835547516381094139939

%N Numerator of the sum of inverse products of parts in all partitions of n.

%H Alois P. Heinz, <a href="/A322364/b322364.txt">Table of n, a(n) for n = 0..505</a>

%H A. Knopfmacher, J. N. Ridley, <a href="http://dx.doi.org/10.1137/0406031">Reciprocal sums over partitions and compositions</a>, SIAM J. Discrete Math. 6 (1993), no. 3, 388-399.

%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa21/aa21123.pdf">On reciprocally weighted partitions</a>, Acta Arithmetica XXI (1972), 379-388.

%H D. Zeilberger, N. Zeilberger, <a href="http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/fcp.html">Fractional Counting of Integer Partitions</a>, 2018.

%F Limit_{n-> infinity} a(n)/(n*A322365(n)) = exp(-gamma) = A080130.

%e 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

%p b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

%p b(n, i-1) +b(n-i, min(i, n-i))/i)

%p end:

%p a:= n-> numer(b(n$2)):

%p seq(a(n), n=0..30);

%Y Denominators: A322365.

%Y Cf. A000041, A006906, A080130, A177208, A177209, A322380, A322381, A323290, A323291, A323339, A323340.

%K nonn,frac

%O 0,3

%A _Alois P. Heinz_, Dec 04 2018

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Last modified April 25 18:12 EDT 2019. Contains 322461 sequences. (Running on oeis4.)