cp's OEIS Frontend

A246939 Number of partitions of n into 7 sorts of parts.

%I A246939 #13 Apr 12 2018 22:23:37
%S A246939 1,7,56,399,2849,19999,140441,983535,6887986,48219486,337559586,
%T A246939 2362943030,16540767131,115785555389,810500055939,5673501716540,
%U A246939 39714520225149,278001650902563,1946011613977669,13622081363362570,95354569947550935,667481990092883448
%N A246939 Number of partitions of n into 7 sorts of parts.
%H A246939 Alois P. Heinz, <a href="/A246939/b246939.txt">Table of n, a(n) for n = 0..1000</a>
%F A246939 G.f.: Product_{i>=1} 1/(1-7*x^i).
%F A246939 a(n) ~ c * 7^n, where c = Product_{k>=1} 1/(1-1/7^k) = 1.1950352398308474540223... . - _Vaclav Kotesovec_, Mar 19 2015
%F A246939 G.f.: Sum_{i>=0} 7^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Apr 12 2018
%p A246939 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246939       b(n, i-1) +`if`(i>n, 0, 7*b(n-i, i))))
%p A246939     end:
%p A246939 a:= n-> b(n$2):
%p A246939 seq(a(n), n=0..25);
%t A246939 (O[x]^20 - 6/QPochhammer[7, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y A246939 Column k=7 of A246935.
%K A246939 nonn
%O A246939 0,2
%A A246939 _Alois P. Heinz_, Sep 08 2014