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A203305 Vandermonde determinant of the first n terms of (1,3,7,15,31,...). 8
1, 2, 48, 64512, 20808990720, 6658450862270054400, 8590449816558320728896700416000, 180165778137909187135292776823951671626301440000, 246665746050863452218796304775365273357060390005370386894553088000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each term divides its successor, as in A028365 and A203307.

LINKS

Table of n, a(n) for n=1..9.

FORMULA

a(n) ~ 2^(n*(n^2 - 1)/3) * QPochhammer(1/2)^n / A335011. - Vaclav Kotesovec, Feb 18 2021

MATHEMATICA

f[j_] := 2^j - 1; z = 15;

v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]

Table[v[n], {n, 1, z}]  (* A203305 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A028365 *)

%/2  (* A203307 *)

Table[(-1)^n * 2^(n*(n+1)*(2*n+1)/6 - 1) / QPochhammer[2, 2, n] * Product[QPochhammer[1/2^k, 2, k], {k, 2, n}], {n, 1, 10}] (* Vaclav Kotesovec, Feb 18 2021 *)

CROSSREFS

Cf. A028365, A203307, A000225, A005329, A335011.

Sequence in context: A098694 A137592 A203778 * A191954 A212170 A057527

Adjacent sequences:  A203302 A203303 A203304 * A203306 A203307 A203308

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 01 2012

STATUS

approved

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Last modified April 19 02:19 EDT 2021. Contains 343105 sequences. (Running on oeis4.)