A222736 Total sum of parts of multiplicity 8 in all partitions of n.

1, 0, 1, 1, 2, 2, 4, 4, 9, 10, 14, 18, 27, 32, 46, 57, 80, 99, 134, 163, 219, 270, 350, 433, 561, 686, 875, 1074, 1349, 1652, 2062, 2509, 3116, 3783, 4650, 5633, 6893, 8305, 10108, 12153, 14709, 17630, 21243, 25371, 30452, 36271, 43335, 51478, 61311, 72598

Offset

8,5

Links

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

Formula

G.f.: (x^8/(1-x^8)^2-x^9/(1-x^9)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 17 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (10368 * 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=8, 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=8..60);

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][[10]]; Table[a[n], {n, 8, 60}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=8 of A222730.

Sequence in context: A324409 A110199 A358429 * A053656 A364752 A035054

Adjacent sequences: A222733 A222734 A222735 * A222737 A222738 A222739

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2013

Status

approved