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A246938 Number of partitions of n into 6 sorts of parts.

%I A246938 #12 Apr 12 2018 22:23:31
%S A246938 1,6,42,258,1590,9582,57786,347010,2083902,12505470,75044202,
%T A246938 450278106,2701739022,16210513806,97263509010,583581545466,
%U A246938 3501491846046,21008954050422,126053739826530,756322456907130,4537934834757702,27227609116759302,163365655261094322
%N A246938 Number of partitions of n into 6 sorts of parts.
%H A246938 Alois P. Heinz, <a href="/A246938/b246938.txt">Table of n, a(n) for n = 0..1000</a>
%F A246938 G.f.: Product_{i>=1} 1/(1-6*x^i).
%F A246938 a(n) ~ c * 6^n, where c = Product_{k>=1} 1/(1-1/6^k) = 1.2411756627857248707756... . - _Vaclav Kotesovec_, Mar 19 2015
%F A246938 G.f.: Sum_{i>=0} 6^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Apr 12 2018
%p A246938 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246938       b(n, i-1) +`if`(i>n, 0, 6*b(n-i, i))))
%p A246938     end:
%p A246938 a:= n-> b(n$2):
%p A246938 seq(a(n), n=0..25);
%t A246938 (O[x]^20 - 5/QPochhammer[6, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y A246938 Column k=6 of A246935.
%K A246938 nonn
%O A246938 0,2
%A A246938 _Alois P. Heinz_, Sep 08 2014