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

8,1

Links

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

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

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);

Crossrefs

Column k=8 of A213177.

Sequence in context: A200018 A019937 A176460 * A228412 A260947 A070489

Adjacent sequences: A320375 A320376 A320377 * A320379 A320380 A320381

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved