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Search: id:A066571
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| A066571 |
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Number of sets of distinct positive integers with arithmetic mean n. |
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+0
4
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| 1, 3, 9, 31, 117, 479, 2061, 9183, 42021, 196239, 931457, 4480531, 21793257, 107004891, 529656765, 2640160039, 13241371629, 66771501151, 338333343825, 1721768732423, 8796192611917, 45096680384635, 231945566136129
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OFFSET
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1,2
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FORMULA
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Sum of coefficient of t^k x^(nk) in Product_{i=1..nk} (1+t*x^i) for k <= 2n-1. - N. J. A. Sloane (njas(AT)research.att.com).
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EXAMPLE
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a(2) = 3 as there are three sets viz. {2), {1,3), {1,2,3}, the arithmetic mean of whose elements is 2.
a(3) = 9: the nine sets are {3}, {1, 5}, {2, 4}, {1, 2, 6}, {1, 3, 5}, {2, 3, 4}, {1, 2, 3, 6}, {1, 2, 4, 5}, {1, 2, 3, 4, 5}
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MAPLE
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g := k->expand(mul(1+t*x^i, i=1..k)); A066571 := proc(n) local k; add(coeff(coeff(g(n*k), t, k), x, n*k), k=1..2*n-1); end;
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CROSSREFS
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Cf. A066572.
Sequence in context: A151036 A073724 A151037 this_sequence A087648 A086616 A040027
Adjacent sequences: A066568 A066569 A066570 this_sequence A066572 A066573 A066574
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KEYWORD
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nonn,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 19 2001
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EXTENSIONS
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Corrected and extended by N. J. A. Sloane (njas(AT)research.att.com), Dec 19 2001
More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jun 19 2002
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 10 2002
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