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 A203239 Odd numbered terms of the sequence whose n-th term is the (n-1)-st elementary symmetric function of (i, 2i, 3i, ..., ni), where i=sqrt(-1). 2
 3, -50, 1764, -109584, 10628640, -1486442880, 283465647360, -70734282393600, 22376988058521600, -8752948036761600000, 4148476779335454720000, -2342787216398718566400000, 1554454559147562279567360000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = (-1)^(n+1)*(2*n)!*Sum_{i=1..2n} 1/i. - Arkadiusz Wesolowski, Mar 25 2013 From Anton Zakharov, Oct 26 2016: (Start) a(n) = (-1)^(n+1)*Sum_{k=1..n} A094310(2n,k). (-1)^(n+1)*a(n) = A000254(2n) (signed bisection of A000254). (End) EXAMPLE The first 10 terms of the "full sequence" are as follows: 1, 3i, -11, -50i, 274, 1764i, -13068, -109584i, 1026576, 10628640i; Abbreviate "elementary symmetric function" as esf. Then, starting with {i, 2i, 3i, 4i, ...}: 0th esf of {i}: 1 1st esf of {i, 2i}: i+2i = 3i 2nd esf of {i, 2i, 3i}: -2-3-6 = -11. For the alternating terms 3i, -50i, ..., see A203240. MATHEMATICA f[k_] := k*I; t[n_] := Table[f[k], {k, 1, n}] a[n_] := SymmetricPolynomial[n - 1, t[n]] Table[a[n], {n, 1, 22}] Table[-I*a[2 n], {n, 1, 22}]     (* A203239 *) Table[a[2 n - 1], {n, 1, 22}]    (* A203240 *) Table[(-1)^(n + 1)*(2*n)!*HarmonicNumber[2*n], {n, 13}] (* Arkadiusz Wesolowski, Mar 25 2013 *) CROSSREFS Cf. A000254, A094310, A165675, A203240. Sequence in context: A326250 A308331 A245141 * A279970 A217767 A185157 Adjacent sequences:  A203236 A203237 A203238 * A203240 A203241 A203242 KEYWORD sign AUTHOR Clark Kimberling, Dec 30 2011 STATUS approved

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Last modified September 21 05:51 EDT 2020. Contains 337267 sequences. (Running on oeis4.)