cp's OEIS Frontend

A111826 Number of partitions of 5*6^n into powers of 6, also equals column 1 of triangle A111825, which shifts columns left and up under matrix 6th power.

%I A111826 #11 Jun 13 2017 22:34:10
%S A111826 1,6,96,6306,1883076,2700393702,19324893252552,709398600017820522,
%T A111826 136347641698786289641932,139389318443495655514432423662,
%U A111826 767442745549858935398537400096197328
%N A111826 Number of partitions of 5*6^n into powers of 6, also equals column 1 of triangle A111825, which shifts columns left and up under matrix 6th power.
%C A111826 Let q=6; 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 A111826 Alois P. Heinz, <a href="/A111826/b111826.txt">Table of n, a(n) for n = 0..40</a>
%F A111826 a(n) = [x^(5*6^n)] 1/Product_{j>=0}(1-x^(6^j)).
%o A111826 (PARI) a(n,q=6)=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 A111826 Cf. A111825 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111831 (q=7), A111836 (q=8).
%K A111826 nonn
%O A111826 0,2
%A A111826 _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005