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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

Alois P. Heinz, Table of n, a(n) for n = 0..505

A. Knopfmacher, J. N. Ridley, Reciprocal sums over partitions and compositions, SIAM J. Discrete Math. 6 (1993), no. 3, 388-399.

D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388.

D. Zeilberger, N. Zeilberger, Fractional Counting of Integer Partitions, 2018.

FORMULA

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

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);

CROSSREFS

Denominators: A322365.

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

Sequence in context: A153285 A083557 A119324 * A250034 A006495 A112286

Adjacent sequences:  A322361 A322362 A322363 * A322365 A322366 A322367

KEYWORD

nonn,frac

AUTHOR

Alois P. Heinz, Dec 04 2018

STATUS

approved

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Last modified March 25 03:50 EDT 2019. Contains 321450 sequences. (Running on oeis4.)