A319335 - OEIS

%I #14 Jan 14 2024 00:14:52

%S 1,3,11,31,187,131,247,1993,4463,3635,395077,24441,81149,10414421,

%T 12868591,10764151,61170133,419426561,353495183,3429826973,

%U 29219934899,5110021867,142319532929,606916707064,87086496509,4426308633083,15954910019953,38414031851849

%N Numerator of the average of the averages of all integer partitions of n.

%H Andrew Howroyd, <a href="/A319335/b319335.txt">Table of n, a(n) for n = 1..500</a>

%e 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.

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

%o (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

%Y Denominators are in A319336.

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

%K nonn,frac

%O 1,2

%A _Gus Wiseman_, Sep 17 2018