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Search: id:A111826
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| A111826 |
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Number of partitions of 5*6^n into powers of 6, also equals column 1 of triangle A111825, which shifts columns left and up under matrix 6-th power. |
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7
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| 1, 6, 96, 6306, 1883076, 2700393702, 19324893252552, 709398600017820522, 136347641698786289641932, 139389318443495655514432423662, 767442745549858935398537400096197328
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Let q=6; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).
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FORMULA
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a(n) = [x^(5*6^n)] 1/Product_{j>=0}(1-x^(6^j)).
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PROGRAM
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(PARI) {a(n, q=6)=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(A[n+2, 2]))}
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CROSSREFS
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Cf. A111825 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111831 (q=7), A111836 (q=8).
Sequence in context: A038094 A126151 A066319 this_sequence A064753 A138913 A127636
Adjacent sequences: A111823 A111824 A111825 this_sequence A111827 A111828 A111829
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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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