A222710 Total number of parts of multiplicity 10 in all partitions of n.

1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 15, 22, 26, 37, 45, 61, 74, 99, 120, 158, 192, 247, 300, 382, 463, 582, 705, 877, 1059, 1309, 1575, 1931, 2319, 2823, 3381, 4094, 4886, 5886, 7007, 8401, 9971, 11905, 14090, 16756, 19781, 23436, 27594, 32586, 38268, 45050

Offset

10,5

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Formula

G.f.: (x^10/(1-x^10)-x^11/(1-x^11))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (220*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=10, 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=10..60);

Mathematica

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 10, 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, 10, 60}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)

Crossrefs

Column k=10 of A197126.

Sequence in context: A206560 A035554 A183567 * A032278 A222738 A005308

Adjacent sequences: A222707 A222708 A222709 * A222711 A222712 A222713

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2013

Status

approved