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A131509
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a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)/6.
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9
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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, 83407045, 102812280, 125842981
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OFFSET
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0,2
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COMMENTS
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See also A131685(k) = smallest positive number m such that c(i) = m (i^1 + 1) (i^2 + 2) ... (i^k+ k) / k! takes integral values for all i>=0. For k=3, A131685(k)=1, which implies that this is a well defined integer sequence. - Alexander R. Povolotsky, May 18 2015
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LINKS
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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, 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, Aug 23 2007
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MATHEMATICA
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Table[x = 3; Product[(n^k) + k, {k, x}]/6, {n, 0, 27}] (* Michael De Vlieger, Apr 24 2015 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 4, 33, 220, 1005, 3456, 9709}, 40] (* Harvey P. Dale, Oct 18 2016 *)
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PROG
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(Maxima) A131509(n):=(n^1 + 1)*(n^2 + 2)*(n^3 + 3)/6$
(PARI) vector(20, n, n--; (n+1)*(n^2+2)*(n^3+3)/3!) \\ Derek Orr, Apr 25 2015
(Magma) [(n^1 + 1)*(n^2 + 2)*(n^3 + 3)/6: n in [0..30]]; // Vincenzo Librandi, Apr 25 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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