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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
 1, 2, 2, -4, 0, 80, -560, 0, 49280, -582400, 0, 117286400, -1947545600, 0, 701372672000, -14996101120000, 0, 8461359915008000, -221282468126720000, 0, 180057738991370240000, -5567466898068275200000, 0, 6171659061668206346240000, -220248990487580966912000000, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See a comment on A282626 on Ramanujan's Master theorem (B) for definite integral, and the Hardy reference. This is the exponential (aka binomial) convolution of A282626. LINKS G. C. Greubel, Table of n, a(n) for n = 0..400 FORMULA a(n) = 2*Product_{j=1..n-1}(n + 2 - 3*j), n >= 1, (empty product = 1) and a(0) = 1. E.g.f.: Square of the e.g.f. of A282626 =   2*x + ((1 + sqrt(1-4*x^3))/2)^(2/3) + ((1 - sqrt(1-4*x^3))/2)^(2/3). MATHEMATICA Table[If[n==0, 1, 2*Product[n+2-3*j, {j, 1, n-1}]], {n, 0, 25}] (* G. C. Greubel, Mar 29 2019 *) PROG (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 (MAGMA) [1, 2] cat [2*(&*[n+2-3*j: j in [1..(n-1)]]): n in [2..25]]; // G. C. Greubel, Mar 29 2019 (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 CROSSREFS Cf. A282626. Sequence in context: A337299 A240491 A113750 * A004565 A068449 A068450 Adjacent sequences:  A282624 A282625 A282626 * A282628 A282629 A282630 KEYWORD sign,easy AUTHOR Wolfdieter Lang, Mar 04 2017 EXTENSIONS Terms a(21) onward added by G. C. Greubel, Mar 30 2019 STATUS approved

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Last modified May 20 01:46 EDT 2022. Contains 353847 sequences. (Running on oeis4.)