A236361 Denominator of the mean of all parts of all partitions of n.

1, 3, 2, 3, 4, 35, 18, 43, 64, 16, 25, 19, 556, 26, 89, 19, 655, 1322, 1749, 463, 1513, 2633, 10206, 941, 16851, 3587, 4549, 4935, 43453, 54563, 68135, 28309, 35122, 65231, 160876, 99007, 242812, 297201, 362587, 10513, 536104, 216597, 785437, 236953, 76063

Offset

1,2

Comments

The arithmetic mean, M(n), of all parts of all partitions of n can be approximated by n^e(n), as typified by these pairs:

n ..... 100 .... 1000 .... 2000 .... 3000 .... 4000 .... 5000

e(n) .. 0.331 .. 0.3410 .. 0.3447 .. 0.3468 .. 0.3483 .. 0.3495

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

M(n) = A066186(n)/A006128(n).

Example

First eight means:  1, 4/3, 3/2, 5/3, 7/4, 66/35, 35/18, 88/43.

Crossrefs

Cf. A006128, A066186, A236360.

Sequence in context: A200599 A239947 A173093 * A227634 A064885 A029618

Adjacent sequences: A236358 A236359 A236360 * A236362 A236363 A236364

Keyword

nonn,frac,easy

Author

Clark Kimberling, Jan 24 2014

Status

approved