A145513 Number of partitions of 10^n into powers of 10.

1, 2, 12, 562, 195812, 515009562, 10837901390812, 1899421190329234562, 2851206628197445401265812, 37421114946843687272702534859562, 4362395890943439751990308572939648140812, 4573514084633441973328831327010967245403925484562, 43557001521047571730475817291330175020887917015964570015812

Offset

0,2

Comments

a(n) = A179051(10^n); for n>0: a(n) = A179052(10^(n-1)). - Reinhard Zumkeller, Jun 27 2010

Links

Alois P. Heinz, Table of n, a(n) for n = 0..45

Formula

a(n) = [x^(10^n)] 1/Product_{j>=0} (1-x^(10^j)).

Example

a(1) = 2, because there are 2 partitions of 10^1 into powers of 10: [1,1,1,1,1,1,1,1,1,1], [10].

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

Mathematica

g[b_, n_, k_] := g[b, n, k] = Module[{t}, 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, 10]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Feb 01 2017, after Alois P. Heinz *)

Prog

(Haskell)
import Data.MemoCombinators (memo2, list, integral)
a145513 n = a145513_list !! n
a145513_list = f [1] where
   f xs = (p' xs $ last xs) : f (1 : map (* 10) xs)
   p' = memo2 (list integral) integral p
   p _ 0 = 1; p [] _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p' ks' (m - k) + p' ks m
-- Reinhard Zumkeller, Nov 27 2015

Crossrefs

Cf. 10th column of A145515, A007318.

Cf. A011557, A002577, A078125.

Sequence in context: A324790 A371202 A050643 * A002860 A108078 A052129

Adjacent sequences: A145510 A145511 A145512 * A145514 A145515 A145516

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2008

Status

approved