A222733 Total sum of parts of multiplicity 5 in all partitions of n.

1, 0, 1, 1, 2, 4, 6, 6, 11, 14, 23, 29, 43, 52, 76, 100, 135, 174, 235, 294, 397, 500, 651, 821, 1060, 1324, 1692, 2107, 2658, 3297, 4139, 5089, 6339, 7778, 9604, 11746, 14425, 17533, 21427, 25960, 31548, 38080, 46070, 55375, 66718, 79957, 95906, 114555

Offset

5,5

Links

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

Formula

G.f.: (x^5/(1-x^5)^2-x^6/(1-x^6)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 11 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (1800 * Pi^2). - Vaclav Kotesovec, May 29 2018

Maple

b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
      add((l->`if`(m=5, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
    end:
a:= n-> b(n, n)[2]:
seq(a(n), n=5..55);

Mathematica

b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[7]]; Table[a[n], {n, 5, 55}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=5 of A222730.

Sequence in context: A066820 A309796 A359671 * A364828 A141677 A087459

Adjacent sequences: A222730 A222731 A222732 * A222734 A222735 A222736

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2013

Status

approved