A320378 Number of parts in all partitions of n with largest multiplicity eight.

8, 0, 9, 9, 19, 19, 40, 40, 81, 93, 140, 173, 267, 315, 461, 572, 779, 970, 1314, 1619, 2152, 2662, 3442, 4265, 5468, 6706, 8502, 10434, 13065, 15969, 19853, 24130, 29769, 36093, 44166, 53357, 64957, 78120, 94585, 113406, 136564, 163163, 195657, 232927, 278157

Offset: 8

Author

Alois P. Heinz, Oct 11 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A213177.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
    end:
a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(8):
seq(a(n), n=8..50);

Formula

a(n) ~ log(3) * exp(4*Pi*sqrt(n/3)/3) / (Pi * sqrt(2) * 3^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018