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A322380 Numerator of the sum of inverse products of parts in all strict partitions of n. 8
1, 1, 1, 5, 7, 37, 79, 173, 101, 127, 1033, 1571, 200069, 2564519, 5126711, 25661369, 532393, 431100529, 1855391, 1533985991, 48977868113, 342880481117, 342289639579, 435979161889, 1308720597671, 373092965489, 7824703695283, 24141028973, 31250466692609 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1268

Andreas B. G. Blobel, An Asymptotic Form of the Generating Function Prod_{k=1,oo} (1+x^k/k), arXiv:1904.07808 [math.CO], 2019.

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)/A322381(n) = exp(-gamma) = A080130.

EXAMPLE

1/1, 1/1, 1/2, 5/6, 7/12, 37/60, 79/120, 173/280, 101/168, 127/210, 1033/1680, 1571/2640, 200069/332640, 2564519/4324320, 5126711/8648640, ... = A322380/A322381

MAPLE

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

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

    end:

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

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

CROSSREFS

Denominators: A322381.

Cf. A000009, A022629, A080130, A177208, A177209, A322364, A322365, A323290, A323291, A323339, A323340.

Sequence in context: A196473 A081851 A192156 * A006067 A244260 A178428

Adjacent sequences:  A322377 A322378 A322379 * A322381 A322382 A322383

KEYWORD

nonn,frac,changed

AUTHOR

Alois P. Heinz, Dec 05 2018

STATUS

approved

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Last modified April 24 10:45 EDT 2019. Contains 322424 sequences. (Running on oeis4.)