A319335 Numerator of the average of the averages of all integer partitions of n.

1, 3, 11, 31, 187, 131, 247, 1993, 4463, 3635, 395077, 24441, 81149, 10414421, 12868591, 10764151, 61170133, 419426561, 353495183, 3429826973, 29219934899, 5110021867, 142319532929, 606916707064, 87086496509, 4426308633083, 15954910019953, 38414031851849

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[Numerator[Mean[Mean/@IntegerPartitions[n]]], {n, 20}]

Prog

(PARI) seq(n)={[numerator(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

Denominators are in A319336.

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

Sequence in context: A163421 A173381 A076477 * A104079 A332264 A089620

Adjacent sequences: A319332 A319333 A319334 * A319336 A319337 A319338

Keyword

nonn,frac

Author

Gus Wiseman, Sep 17 2018

Status

approved