A222707 Total number of parts of multiplicity 7 in all partitions of n.

1, 0, 1, 1, 2, 2, 4, 5, 8, 9, 14, 17, 25, 30, 43, 53, 72, 88, 118, 145, 190, 234, 301, 370, 471, 575, 724, 884, 1102, 1339, 1657, 2007, 2465, 2975, 3630, 4369, 5301, 6355, 7672, 9171, 11018, 13126, 15706, 18655, 22231, 26329, 31260, 36920, 43688, 51454, 60693

Offset

7,5

Links

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

Formula

G.f.: (x^7/(1-x^7)-x^8/(1-x^8))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (112*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 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]], 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, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 7, l + {0, l[[1]]}, l]][b[n - p*m, p - 1]], {m, 0, n/p}]]];
a[n_] := b[n, n][[2]];
Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)

Crossrefs

Column k=7 of A197126.

Sequence in context: A069906 A304332 A183564 * A326525 A326630 A317810

Adjacent sequences: A222704 A222705 A222706 * A222708 A222709 A222710

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2013

Status

approved