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 A262396 Product of the sums and differences of the square roots of the first n positive integers, combined in all possible ways. 1
 1, -1, 1, 64, 4096, 23323703841, 63703464216016403230349121, 316699666163357097153212433469030615484754548657341071360000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The series increases rapidly and the next number in the sequence has 135 decimal digits. Each element for n>1 is necessarily both an integer and a perfect square, the square roots being 1, 8, 64, 152721, 7981444995489, 562760753929551396141111705600, ... LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10 EXAMPLE a(0) = 1 = (empty product). a(1) = -1 = (sqrt(1)) * (-sqrt(1)). a(2) = 1 = (1+sqrt(2)) * (1-sqrt(2)) * (-1+sqrt(2)) * (-1-sqrt(2)). a(3) = 64 = (1+sqrt(2)+sqrt(3)) * (1+sqrt(2)-sqrt(3)) * (1-sqrt(2)+sqrt(3)) * (1-sqrt(2)-sqrt(3)) * (-1+sqrt(2)+sqrt(3)) * (-1+sqrt(2)-sqrt(3)) * (-1-sqrt(2)+sqrt(3)) * (-1-sqrt(2)-sqrt(3)). MAPLE s:= proc(n) option remember; `if`(n<2, [1, -1][1..2*n],        map(x-> [x+sqrt(n), x-sqrt(n)][], s(n-1)))     end: a:= n-> expand(mul(t, t=s(n))): seq(a(n), n=0..7);  # Alois P. Heinz, Sep 21 2015 CROSSREFS Sequence in context: A144320 A324493 A324490 * A318015 A320401 A203438 Adjacent sequences:  A262393 A262394 A262395 * A262397 A262398 A262399 KEYWORD sign AUTHOR Mark Bradley, Sep 21 2015 STATUS approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)