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Search: id:A131509
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| A131509 |
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a(n) = (n^1 + 1)*(n^2 + 2)*(n^3 + 3)/6. |
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+0
3
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| 1, 4, 33, 220, 1005, 3456, 9709, 23528, 50985, 101260, 187561, 328164, 547573, 877800, 1359765, 2044816, 2996369, 4291668, 6023665, 8303020, 11260221, 15047824, 19842813, 25849080, 33300025, 42461276, 53633529, 67155508
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Following my conjecture, computations by Peter J. C. Moses, mediation by Clark Kimberling and helpful comments from George E. Andrews, it is now known that a(n) = (n^1 + 1)*(n^2 + 2)*(n^3 + 3)*...*(n^k + k)/k! is an integer-valued sequence if and only if k belongs to {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 18, 19, 20, 21}.
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FORMULA
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G.f.: (1 - 3x + 26x^2 +38x^3 +53x^4 +5x^5)/(1-x)^7. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 23 2007
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MAPLE
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p:=proc(n, i) mul( n^j+j, j=1..i)/i!; end; [seq(p(n, 3), n=0..30)];
seq((1/6)*(n+1)*(n^2+2)*(n^3+3), n=0..25); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 23 2007
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CROSSREFS
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Cf. A000027 (k=1), A064808 (k=2), this sequence (k=3), A129995 (k=4), A131675 (k=5), ..., A131680 (k=10).
Sequence in context: A095671 A013192 A097705 this_sequence A081007 A088317 A041024
Adjacent sequences: A131506 A131507 A131508 this_sequence A131510 A131511 A131512
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KEYWORD
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nonn
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AUTHOR
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Alexander Povolotsky (pevnev(AT)juno.com), Aug 13 2007, Aug 25 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 21 2007
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