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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

Table of n, a(n) for n=1..11.

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 February 21 10:51 EST 2018. Contains 299390 sequences. (Running on oeis4.)