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A111832 Number of partitions of 7^n into powers of 7, also equals the row sums of triangle A111830, which shifts columns left and up under matrix 7th power.

%I A111832 #13 Jun 13 2017 22:36:43
%S A111832 1,2,9,205,24901,16077987,58169810617,1226373476385199,
%T A111832 154912862345527456431,119679779055077323244243580,
%U A111832 574461679441277269788798742908435,17346328772332966415272910459727649244337,3328366331331467859745524303574824288197338547909
%N A111832 Number of partitions of 7^n into powers of 7, also equals the row sums of triangle A111830, which shifts columns left and up under matrix 7th power.
%H A111832 Alois P. Heinz, <a href="/A111832/b111832.txt">Table of n, a(n) for n = 0..28</a>
%F A111832 a(n) = [x^(7^n)] 1/Product_{j>=0}(1-x^(7^j)).
%o A111832 (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(sum(k=0,n,A[n+1,k+1])))
%Y A111832 Cf. A111830, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111837 (q=8). Column 7 of A145515.
%K A111832 nonn
%O A111832 0,2
%A A111832 _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005