A182804 Number of 9-core partitions of n.

1, 1, 2, 3, 5, 7, 11, 15, 22, 21, 33, 38, 50, 56, 72, 77, 96, 99, 142, 139, 177, 180, 228, 229, 288, 284, 357, 343, 430, 410, 519, 491, 615, 588, 745, 714, 832, 811, 1007, 939, 1152, 1077, 1310, 1215, 1456, 1426, 1686, 1580, 1887, 1778, 2137

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

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

Euler transform of period 9 sequence [1,1,1,1,1,1,1,1,-8, .. ].

Maple

with(numtheory): A:= proc(n, t) option remember; local d, j; `if`(n=0, 1, add(add(`if`(t=0 or irem(d, t)=0, d-d*t, d), d=divisors(j)) *A(n-j, t), j=1..n)/n) end: seq(A(n, 9), n=0..50);

Mathematica

A[n_, t_] := A[n, t] = If[n == 0, 1, Sum[Sum[If[t == 0 || Mod[d, t] == 0, d - d*t, d], {d, Divisors[j]}]*A[n - j, t], {j, 1, n}]/n] ;
Table[A[n, 9], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Crossrefs

9th column of A175595.

Sequence in context: A363231 A184643 A307547 * A242695 A319473 A085894

Adjacent sequences: A182801 A182802 A182803 * A182805 A182806 A182807

Keyword

nonn

Author

Alois P. Heinz, Dec 03 2010

Status

approved