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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.
6
1, 2, 7, 82, 3707, 642457, 446020582, 1288155051832, 15905066118254957, 856874264098480364332, 204616369654716156089739332, 219286214391142987407272329973707, 1065403165201779499307991460987124895582, 23663347632778954225192551079067428619449114332
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved