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

%I A246942 #9 Nov 21 2015 00:46:09
%S A246942 1,10,110,1110,11210,112210,1123310,11234310,112355410,1123567410,
%T A246942 11235798510,112358120510,1123582462610,11235825994610,
%U A246942 112358272546710,1123582739289710,11235827519061810,112358275329114810,1123582754554197910,11235827546928570910
%N A246942 Number of partitions of n into 10 sorts of parts.
%H A246942 Alois P. Heinz, <a href="/A246942/b246942.txt">Table of n, a(n) for n = 0..1000</a>
%F A246942 G.f.: Product_{i>=1} 1/(1-10*x^i).
%F A246942 a(n) ~ c * 10^n, where c = Product_{k>=1} 1/(1-1/10^k) = 1.12358275484865251117... . - _Vaclav Kotesovec_, Mar 19 2015
%p A246942 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246942       b(n, i-1) +`if`(i>n, 0, 10*b(n-i, i))))
%p A246942     end:
%p A246942 a:= n-> b(n$2):
%p A246942 seq(a(n), n=0..25);
%t A246942 (O[x]^20 - 9/QPochhammer[10, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y A246942 Column k=10 of A246935.
%K A246942 nonn
%O A246942 0,2
%A A246942 _Alois P. Heinz_, Sep 08 2014