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

0,2

Links

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

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

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 *)

Crossrefs

Column k=9 of A246935.

Sequence in context: A054616 A344068 A052386 * A186510 A158609 A229250

Adjacent sequences: A246938 A246939 A246940 * A246942 A246943 A246944

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved