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 A286723 Column k = 1 of the triangle A225471; Sheffer ((1 - 3*x)^(-3/4), (-1/4)*log(1 - 4*x)). 0
 1, 10, 131, 2196, 45189, 1105182, 31354119, 1012861224, 36717532425, 1476342400050, 65212709985675, 3139386801018300, 163605030141437325, 9176588125543758150, 551225830134140520975, 35305848011347321438800, 2401944921672748059294225, 172980447467901106243829850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is, for n >= 1, the total volume of the binomial(n+1, n) rectangular polytopes (hyper-cuboids) built from n orthogonal vectors with lengths of the sides from the set {3 + 4*j | j=0..n}. See the formula a(n) = sigma[4,3]^{(n+1)}_n and an example below. LINKS Table of n, a(n) for n=0..17. FORMULA a(n) = A225471(n+1, 1), n >= 1. E.g.f.: (d/dx) ((1 - 4*x)^(-3/4)*((-1/4)*log(1 - 4*x))) = (4 - 3*log(1-4*x)) / (4*(1-4*x)^(7/4)). a(n) = sigma[4,3]^{(n+1)}_n, n >= 0, with the elementary symmetric function sigma[4,3]^{(n+1)}_n of degree n of the n+1 numbers 3, 7, 11, ..., (1 + 4*n), and sigma[4,3]^{(n+1)}_0 := 1. EXAMPLE a(2) = 131 because sigma[4,3]^{(3)}_2 = 3*(7 + 11) + 7*11 = 131. There are three rectangles (2D rectangular polytopes) built from two orthogonal vectors of different lengths from the set of {3,7,11} of total area 131. CROSSREFS Cf. A008545 (k=0), A225471. Sequence in context: A281395 A268786 A284196 * A239814 A166771 A264279 Adjacent sequences: A286720 A286721 A286722 * A286724 A286725 A286726 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, May 29 2017 STATUS approved

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Last modified October 3 07:13 EDT 2023. Contains 365842 sequences. (Running on oeis4.)