A111822 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.

1, 2, 7, 82, 3707, 642457, 446020582, 1288155051832, 15905066118254957, 856874264098480364332, 204616369654716156089739332, 219286214391142987407272329973707, 1065403165201779499307991460987124895582, 23663347632778954225192551079067428619449114332

Offset: 0

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..55

Crossrefs

Cf. A111820, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111827 (q=6), A111832 (q=7), A111837 (q=8).

Column k=5 of A145515.

Programs

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])))

Formula

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