A246942 Number of partitions of n into 10 sorts of parts.

1, 10, 110, 1110, 11210, 112210, 1123310, 11234310, 112355410, 1123567410, 11235798510, 112358120510, 1123582462610, 11235825994610, 112358272546710, 1123582739289710, 11235827519061810, 112358275329114810, 1123582754554197910, 11235827546928570910

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=10 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, 10*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 9/QPochhammer[10, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

G.f.: Product_{i>=1} 1/(1-10*x^i).

a(n) ~ c * 10^n, where c = Product_{k>=1} 1/(1-1/10^k) = 1.12358275484865251117... . - Vaclav Kotesovec, Mar 19 2015