A320375 Number of parts in all partitions of n with largest multiplicity five.

5, 0, 6, 6, 13, 18, 34, 35, 66, 82, 120, 154, 230, 286, 408, 514, 699, 886, 1189, 1485, 1949, 2441, 3136, 3906, 4980, 6159, 7757, 9555, 11908, 14600, 18062, 22000, 27028, 32804, 39996, 48327, 58614, 70489, 85036, 101876, 122284, 145943, 174419, 207354, 246804

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Formula

a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(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])(5):
seq(a(n), n=5..50);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0},        Sum[Function[l, {0, l[[1]] j} + l][b[n - i j, i - 1, k]], {j, 0, Min[n/i, k]}]]];
a[n_] := With[{k = 5}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
a /@ Range[5, 50] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A213177.

Sequence in context: A353876 A166126 A265011 * A361918 A200419 A271522

Adjacent sequences: A320372 A320373 A320374 * A320376 A320377 A320378

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved