A111822 - OEIS

%I #17 Nov 28 2017 11:46:49

%S 1,2,7,82,3707,642457,446020582,1288155051832,15905066118254957,

%T 856874264098480364332,204616369654716156089739332,

%U 219286214391142987407272329973707,1065403165201779499307991460987124895582,23663347632778954225192551079067428619449114332

%N Number of partitions of 5^n into powers of 5, also equals the row sums of triangle A111820, which shifts columns left and up under matrix 5th power.

%H Alois P. Heinz, <a href="/A111822/b111822.txt">Table of n, a(n) for n = 0..55</a>

%F a(n) = [x^(5^n)] 1/Product_{j>=0}(1-x^(5^j)).

%o (PARI) a(n,q=5)=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 Cf. A111820, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111827 (q=6), A111832 (q=7), A111837 (q=8).

%Y Column k=5 of A145515.

%K nonn

%O 0,2

%A _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005