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Search: id:A111822
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| A111822 |
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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 5-th power. |
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6
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| 1, 2, 7, 82, 3707, 642457, 446020582, 1288155051832, 15905066118254957, 856874264098480364332, 204616369654716156089739332, 219286214391142987407272329973707
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = [x^(5^n)] 1/Product_{j>=0}(1-x^(5^j)).
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PROGRAM
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(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])))}
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CROSSREFS
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Cf. A111820, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111827 (q=6), A111832 (q=7), A111837 (q=8).
Sequence in context: A128293 A071409 A135756 this_sequence A062764 A163855 A041291
Adjacent sequences: A111819 A111820 A111821 this_sequence A111823 A111824 A111825
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KEYWORD
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nonn
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AUTHOR
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Gottfried Helms (helms(AT)uni-kassel.de) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2005
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