A145514 Number of partitions of n^n into powers of n, also diagonal of A145515 and A196879.

1, 1, 4, 23, 1086, 642457, 6188114528, 1226373476385199, 6071277235712979102634, 884267692532264259002637317099, 4362395890943439751990308572939648140812, 824887275128335259519795007492785652798382136996397

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..36

Formula

a(n) = [x^(n^n)] 1/Product_{j>=0}(1-x^(n^j)), n>1.

Example

a(2) = 4, because there are 4 partitions of 2^2=4 into powers of 2: [1,1,1,1], [1,1,2], [2,2], [4].

Maple

g:= proc(b, n, k) option remember; local t; if b<0 then 0 elif b=0 or n=0 or k<=1 then 1 elif b>=n then add(g(b-t, n, k) *binomial(n+1, t) *(-1)^(t+1), t=1..n+1); else g(b-1, n, k) +g(b*k, n-1, k) fi end: a:= n-> g(1, n, n): seq(a(n), n=0..13);

Mathematica

g[b_, n_, k_] := g[b, n, k] = Which[b<0, 0, b == 0 || n == 0 || k <= 1, 1, b >= n, Sum[g[b-t, n, k] *Binomial[n+1, t]*(-1)^(t+1), {t, 1, n+1}], True, g[b-1, n, k] + g[b*k, n-1, k]]; a[n_] := g[1, n, n]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *)

Crossrefs

Cf. A145515, A196879, A007318.

Sequence in context: A316240 A305948 A317211 * A305665 A319145 A024543

Adjacent sequences: A145511 A145512 A145513 * A145515 A145516 A145517

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2008

Status

approved