A222734 Total sum of parts of multiplicity 6 in all partitions of n.

1, 0, 1, 1, 2, 2, 6, 6, 9, 12, 18, 22, 36, 43, 62, 77, 107, 133, 186, 229, 306, 384, 499, 621, 810, 999, 1277, 1582, 1997, 2453, 3088, 3776, 4698, 5742, 7088, 8618, 10592, 12824, 15654, 18910, 22955, 27615, 33400, 40028, 48174, 57593, 69018, 82231, 98225

Offset

6,5

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

G.f.: (x^6/(1-x^6)^2-x^7/(1-x^7)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 13 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (3528 * 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=6, 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=6..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][[8]]; Table[a[n], {n, 6, 55}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=6 of A222730.

Sequence in context: A010762 A055993 A309912 * A151888 A320046 A289835

Adjacent sequences: A222731 A222732 A222733 * A222735 A222736 A222737

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2013

Status

approved