A222735 Total sum of parts of multiplicity 7 in all partitions of n.

1, 0, 1, 1, 2, 2, 4, 6, 9, 10, 16, 20, 29, 36, 53, 66, 91, 112, 152, 190, 251, 315, 409, 510, 655, 809, 1029, 1271, 1602, 1967, 2457, 3009, 3729, 4543, 5595, 6801, 8321, 10069, 12258, 14783, 17906, 21511, 25947, 31073, 37315, 44542, 53285, 63415, 75587, 89687

Offset

7,5

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

G.f.: (x^7/(1-x^7)^2-x^8/(1-x^8)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 15 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (6272 * 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=7, 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=7..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][[9]]; Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=7 of A222730.

Sequence in context: A231187 A055529 A337723 * A299408 A338937 A319381

Adjacent sequences: A222732 A222733 A222734 * A222736 A222737 A222738

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2013

Status

approved