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

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn
• frac

Examples

			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.
		

Links

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

Crossrefs

Denominators are in A319336.

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

Programs

Mathematica

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

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