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Search: id:A111821
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| A111821 |
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Number of partitions of 4*5^n into powers of 5, also equals column 1 of triangle A111820, which shifts columns left and up under matrix 5-th power. |
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8
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| 1, 5, 55, 2055, 291430, 165397680, 390075741430, 3927972221522680, 172358768282285194555, 33479766506261422878944555, 29150234311482124092454001991430
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OFFSET
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0,2
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COMMENT
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Let q=5; 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^(4*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(A[n+2, 2]))}
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CROSSREFS
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Cf. A111820 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111826 (q=6), A111831 (q=7), A111836 (q=8).
Sequence in context: A126456 A126157 A105715 this_sequence A068666 A082780 A063855
Adjacent sequences: A111818 A111819 A111820 this_sequence A111822 A111823 A111824
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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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