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A145512 Number of partitions of 9^n into powers of 9. 2
1, 2, 11, 416, 106121, 184174976, 2301962201813, 215628573640652084, 155675227490715893806397, 884267692532264259002637317099, 40145668231846724902431764046045910334, 14749630591672953206497180542249687004502709494 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

EXAMPLE

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].

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);

CROSSREFS

Cf. 9th column of A145515, A007318.

Sequence in context: A309068 A015180 A052290 * A013046 A012950 A012979

Adjacent sequences:  A145509 A145510 A145511 * A145513 A145514 A145515

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 11 2008

STATUS

approved

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Last modified July 30 07:58 EDT 2021. Contains 346348 sequences. (Running on oeis4.)