cp's OEIS Frontend

A111831 Number of partitions of 6*7^n into powers of 7, also equals column 1 of triangle A111830, which shifts columns left and up under matrix 7th power.

%I A111831 #11 Jun 13 2017 22:36:45
%S A111831 1,7,154,16275,9106461,28543862991,521136519414483,
%T A111831 56980036448207052005,38084892600214854893482284,
%U A111831 158081960770204032330986210466109,4125860571927530263431055188002578191656
%N A111831 Number of partitions of 6*7^n into powers of 7, also equals column 1 of triangle A111830, which shifts columns left and up under matrix 7th power.
%C A111831 Let q=7; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).
%H A111831 Alois P. Heinz, <a href="/A111831/b111831.txt">Table of n, a(n) for n = 0..40</a>
%F A111831 a(n) = [x^(6*7^n)] 1/Product_{j>=0}(1-x^(7^j)).
%o A111831 (PARI) a(n,q=7)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+2,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i || j==1,B[i,j]=1,B[i,j]=(A^q)[i-1,j-1]);));A=B); return(A[n+2,2]))
%Y A111831 Cf. A111830 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111826 (q=6), A111836 (q=8).
%K A111831 nonn
%O A111831 0,2
%A A111831 _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005