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 A130032 Row sums of unsigned triangle A129467. 5
 1, 1, 3, 21, 273, 5733, 177723, 7642089, 435599073, 31798732329, 2893684641939, 321198995255229, 42719466368945457, 6706956219924436749, 1227372988246171925067, 258975700519942276189137, 62413143825306088561582017, 17038788264308562177311890641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS M. Bruschi, F. Calogero and R. Droghei, Proof of certain Diophantine conjectures and identification of remarkable classes of orthogonal polynomials, J. Physics A, 40(2007), pp. 3815-3829. FORMULA a(n) = sum(|A129467(n,m)|, m=0..n), n>=0. For n > 0, a(n) = n! * Product_{k=1..n}[Gamma(k + 1/k)/Gamma(k - 1 + 1/k)]. - Gerald McGarvey, Nov 05 2007 a(n) = product(k^2-k+1,k=0..n). - Gary Detlefs, Mar 04 2012 a(n) ~ c n! (n-1)! for c = prod(k>=1, 1+1/(k^2+k)) = 2.428189792... [Charles R Greathouse IV, Mar 04 2012], c = cosh(sqrt(3)*Pi/2)/Pi. - Vaclav Kotesovec, Aug 24 2016 G.f.: 1+x + 3*x^2/(Q(0)-3*x), where Q(k) = 1 + x*(k^2+3*k+3) - x*(k^2+5*k+7)/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 15 2013 MATHEMATICA Round@Table[Cosh[Sqrt[3] Pi/2] Gamma[n + 1/2 + I Sqrt[3]/2] Gamma[n + 1/2 - I Sqrt[3]/2]/Pi, {n, 0, 20}] (* Vladimir Reshetnikov, Aug 23 2016 *) PROG (PARI) a(n)=prod(k=1, n, k^2-k+1) \\ Charles R Greathouse IV, Mar 04 2012 CROSSREFS Cf. A130031 (signed row sums). a(n+1), n>=0, also row sums of unsigned triangle A130559. Sequence in context: A227820 A336809 A066206 * A174967 A126461 A000681 Adjacent sequences: A130029 A130030 A130031 * A130033 A130034 A130035 KEYWORD nonn,easy AUTHOR Wolfdieter Lang May 04 2007, Jun 04 2010 STATUS approved

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Last modified March 21 19:35 EDT 2023. Contains 361410 sequences. (Running on oeis4.)