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 A066571 Number of sets of positive integers with arithmetic mean n. 7
 1, 3, 9, 31, 117, 479, 2061, 9183, 42021, 196239, 931457, 4480531, 21793257, 107004891, 529656765, 2640160039, 13241371629, 66771501151, 338333343825, 1721768732423, 8796192611917, 45096680384635, 231945566136129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Franklin T. Adams-Watters, Sep 13 2011: (Start) If we use nonnegative integers instead of positive integers, we get this sequence shifted left (i.e., with offset 0). The largest number that can be included in set of positive integers with mean n is the triangular number n*(n+1)/2 = A000217(n). All values are odd. Sets including n are paired with the same set with n removed, with exception of {n}, as the empty set has no average. (End) LINKS FORMULA Sum of coefficient of t^k x^(n*k) in Product_{i=1..n*k} (1+t*x^i) for k <= 2*n-1. - N. J. A. Sloane. EXAMPLE 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} MAPLE 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; MATHEMATICA g[k_] := Expand[Product[1 + t*x^i, {i, 1, k}]]; a[n_] := Sum[Coefficient[ Coefficient[g[n*k], t, k], x, n*k], {k, 1, 2*n - 1}]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 10}] (* Jean-François Alcover, Feb 10 2018, translated from Maple *) PROG (Haskell) a066571 n = f [1..] 1 n 0 where    f (k:ks) l nl x      | y > nl  = 0      | y < nl  = f ks (l + 1) (nl + n) y + f ks l nl x      | otherwise = if y `mod` l == 0 then 1 else 0      where y = x + k -- Reinhard Zumkeller, Feb 13 2013 CROSSREFS Cf. A066572, A000217. Cf. A072701, A164283. Sequence in context: A151036 A073724 A151037 * A087648 A086616 A040027 Adjacent sequences:  A066568 A066569 A066570 * A066572 A066573 A066574 KEYWORD nonn,nice AUTHOR Amarnath Murthy, Dec 19 2001 EXTENSIONS Corrected and extended by N. J. A. Sloane, Dec 19 2001 More terms from Naohiro Nomoto, Jun 19 2002 More terms from David Wasserman, Sep 10 2002 STATUS approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)