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Search: id:A130714
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| A130714 |
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Number of partitions of n such that every part divides the largest part and such that the smallest part divides every part. |
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+0
1
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| 1, 2, 3, 5, 6, 10, 11, 16, 19, 26, 27, 41, 42, 55, 64, 81, 83, 114, 116, 151, 168, 202, 210, 277, 289, 348, 382, 460, 478, 604, 623, 747, 812, 942, 1006, 1223, 1269, 1479, 1605, 1870, 1959, 2329, 2434, 2818, 3056, 3458, 3653, 4280, 4493, 5130, 5507, 6231, 6580
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OFFSET
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1,2
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FORMULA
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G.f.: Sum_{i>=0} Sum_(j>0} x^(j+i*j)/Product_{k|i} (1-x^(j*k)).
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MAPLE
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A130714 := proc(n) local gf, den, i, k, j ; gf := 0 ; for i from 0 to n do for j from 1 to n/(1+i) do den := 1 ; for k in numtheory[divisors](i) do den := den*(1-x^(j*k)) ; od ; gf := taylor(gf+x^(j+i*j)/den, x=0, n+1) ; od ; od: coeftayl(gf, x=0, n) ; end: seq(A130714(n), n=1..60) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007
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CROSSREFS
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Adjacent sequences: A130711 A130712 A130713 this_sequence A130715 A130716 A130717
Sequence in context: A018396 A003238 A051839 this_sequence A130689 A024560 A000039
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 02 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007
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