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 A203421 Reciprocal of Vandermonde determinant of (1,1/2,...,1/n). 7
 1, -2, -18, 1152, 720000, -5598720000, -658683809280000, 1381360067999170560000, 59463021447701323327733760000, -59463021447701323327733760000000000000, -1542317635347398938581016812202229760000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each term divides its successor, as in A000169. LINKS FORMULA G.f.: G(0)/(2*x) -1/x, where G(k)= 1 + 1/(1 - x/(x + (2*k+1)/((2*k+1)^(2*k+1))/(1 + 1/(1 - x/(x - (2*k+2)/((2*k+2)^(2*k+2))/G(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013 a(n) = (-1)^floor(n/2) * hyperfactorial(n)/n! = A057077(n) * A002109(n)/n!. - Paul J. Harvey, Feb 08 2014 MATHEMATICA f[j_] := 1/j; z = 12; v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}] Table[v[n], {n, 1, z}] 1/%  (* A203421 *) Table[v[n]/v[n + 1], {n, 1, z - 1}]  (* A000169 signed *) (* a simpler program: *) Table[(-1)^Floor[n/2]*Product[(k + 1)^k, {k, 0, n - 1}], {n, 1, 10}] (* Vaclav Kotesovec, Oct 18 2015 *) CROSSREFS Cf. A000169, A000027. Sequence in context: A268051 A268074 A202544 * A139111 A090766 A069651 Adjacent sequences:  A203418 A203419 A203420 * A203422 A203423 A203424 KEYWORD sign AUTHOR Clark Kimberling, Jan 02 2012 STATUS approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)