A319336 Denominator of the average of the averages of all integer partitions of n.

1, 2, 6, 15, 84, 55, 100, 770, 1680, 1323, 141120, 8470, 27720, 3474900, 4228224, 3468465, 19459440, 131030900, 109156320, 1042578108, 8779605120, 1514663280, 41736380400, 175685635125, 24960905112, 1254125149200, 4476730258000, 10664476594200, 73326164511600

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Example

The sequence of average averages begins: 1, 3/2, 11/6, 31/15, 187/84, 131/55, 247/100, 1993/770, 4463/1680, 3635/1323.

Mathematica

Table[Denominator[Mean[Mean/@IntegerPartitions[n]]], {n, 20}]

Prog

(PARI) seq(n)={[denominator(poldegree(p)*subst(intformal(p/y)/p, y, 1)) | p <- Vec(-1+1/prod(k=1, n, 1 - x^k*y + O(x*x^n)))]} \\ Andrew Howroyd, Sep 19 2018

Crossrefs

Numerators are in A319335.

Cf. A056239, A067538, A237984, A296150, A316313, A316314, A316440.

Sequence in context: A244443 A346555 A356223 * A007709 A190339 A078328

Adjacent sequences: A319333 A319334 A319335 * A319337 A319338 A319339

Keyword

nonn,frac

Author

Gus Wiseman, Sep 17 2018

Status

approved