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

0,2

Links

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

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

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 *)

Crossrefs

Column k=10 of A246935.

Sequence in context: A289046 A284021 A105279 * A289371 A289100 A289400

Adjacent sequences: A246939 A246940 A246941 * A246943 A246944 A246945

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved