A222737 Total sum of parts of multiplicity 9 in all partitions of n.

1, 0, 1, 1, 2, 2, 4, 4, 7, 10, 14, 16, 25, 30, 42, 53, 71, 88, 121, 148, 195, 241, 312, 384, 494, 605, 765, 943, 1179, 1441, 1796, 2181, 2694, 3273, 4011, 4849, 5922, 7130, 8652, 10398, 12552, 15021, 18072, 21558, 25816, 30729, 36649, 43480, 51705, 61163

Offset

9,5

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

G.f.: (x^9/(1-x^9)^2-x^10/(1-x^10)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 19 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (16200 * 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=9, 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=9..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][[11]]; Table[a[n], {n, 9, 60}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=9 of A222730.

Sequence in context: A253412 A291148 A032190 * A005852 A370591 A274625

Adjacent sequences: A222734 A222735 A222736 * A222738 A222739 A222740

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2013

Status

approved