A145512 Number of partitions of 9^n into powers of 9.

1, 2, 11, 416, 106121, 184174976, 2301962201813, 215628573640652084, 155675227490715893806397, 884267692532264259002637317099, 40145668231846724902431764046045910334, 14749630591672953206497180542249687004502709494

Offset: 0

Author

Alois P. Heinz, Oct 11 2008

Keywords

• nonn

Examples

			a(1) = 2, because there are 2 partitions of 9^1 into powers of 9: [1,1,1,1,1,1,1,1,1], [9].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..47

Crossrefs

Cf. 9th column of A145515, A007318.

Programs

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,9): seq(a(n), n=0..13);

Formula

a(n) = [x^(9^n)] 1/Product_{j>=0}(1-x^(9^j)).