A320379 Number of parts in all partitions of n with largest multiplicity nine.

9, 0, 10, 10, 21, 21, 44, 44, 80, 101, 152, 178, 279, 330, 476, 594, 813, 1004, 1359, 1669, 2208, 2743, 3540, 4365, 5610, 6876, 8697, 10669, 13349, 16290, 20258, 24603, 30334, 36773, 44999, 54312, 66122, 79490, 96214, 115337, 138887, 165891, 198941, 236783

Offset

9,1

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

a(n) ~ log(10) * exp(Pi*sqrt(3*n/5)) / (2 * Pi * 15^(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])(9):
seq(a(n), n=9..50);

Crossrefs

Column k=9 of A213177.

Sequence in context: A151949 A341486 A349825 * A308102 A338016 A062047

Adjacent sequences: A320376 A320377 A320378 * A320380 A320381 A320382

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved