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

Author

Clark Kimberling, Jan 24 2014

Keywords

• nonn
• frac
• easy

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

Examples

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

Links

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

Crossrefs

Cf. A006128, A066186, A236360.

Formula

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