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

0,2

Links

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

Formula

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

Prog

(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])))

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.

Sequence in context: A263368 A208806 A319144 * A062764 A163855 A268299

Adjacent sequences: A111819 A111820 A111821 * A111823 A111824 A111825

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved