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A282627 Exponential expansion of the square of the real root y = y(x) of y^3 - 3*x*y - 1. 2

%I

%S 1,2,2,-4,0,80,-560,0,49280,-582400,0,117286400,-1947545600,0,

%T 701372672000,-14996101120000,0,8461359915008000,-221282468126720000,

%U 0,180057738991370240000,-5567466898068275200000,0,6171659061668206346240000,-220248990487580966912000000,0

%N Exponential expansion of the square of the real root y = y(x) of y^3 - 3*x*y - 1.

%C See a comment on A282626 on Ramanujan's Master theorem (B) for definite integral, and the Hardy reference.

%C This is the exponential (aka binomial) convolution of A282626.

%H G. C. Greubel, <a href="/A282627/b282627.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) = 2*Product_{j=1..n-1}(n + 2 - 3*j), n >= 1, (empty product = 1) and a(0) = 1.

%F E.g.f.: Square of the e.g.f. of A282626 =

%F 2*x + ((1 + sqrt(1-4*x^3))/2)^(2/3) + ((1 - sqrt(1-4*x^3))/2)^(2/3).

%t Table[If[n==0,1,2*Product[n+2-3*j, {j,1,n-1}]], {n,0,25}] (* _G. C. Greubel_, Mar 29 2019 *)

%o (PARI) vector(25, n, n--; if(n==0,1,2*prod(j=1,n-1, (n+2-3*j)))) \\ _G. C. Greubel_, Mar 29 2019

%o (MAGMA) [1,2] cat [2*(&*[n+2-3*j: j in [1..(n-1)]]): n in [2..25]]; // _G. C. Greubel_, Mar 29 2019

%o (Sage) [1] + [2*product(n+2-3*j for j in (1..(n-1))) for n in (1..25)] # _G. C. Greubel_, Mar 29 2019

%Y Cf. A282626.

%K sign,easy

%O 0,2

%A _Wolfdieter Lang_, Mar 04 2017

%E Terms a(21) onward added by _G. C. Greubel_, Mar 30 2019

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Last modified June 28 01:48 EDT 2022. Contains 354903 sequences. (Running on oeis4.)