A246941 Number of partitions of n into 9 sorts of parts.

1, 9, 90, 819, 7461, 67239, 606051, 5455359, 49106502, 441967518, 3977783082, 35800130448, 322201861893, 2899817511237, 26098363809063, 234885281153616, 2113967586352095, 19025708339182545, 171231375557145825, 1541082380573345274, 13869741429702220707

Offset: 0

Author

Alois P. Heinz, Sep 08 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=9 of A246935.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1) +`if`(i>n, 0, 9*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 8/QPochhammer[9, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

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

a(n) ~ c * 9^n, where c = Product_{k>=1} 1/(1-1/9^k) = 1.1408227572644372820166... . - Vaclav Kotesovec, Mar 19 2015

G.f.: Sum_{i>=0} 9^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Oct 18 2018