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A130032
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Row sums of unsigned triangle A129467.
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5
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1, 1, 3, 21, 273, 5733, 177723, 7642089, 435599073, 31798732329, 2893684641939, 321198995255229, 42719466368945457, 6706956219924436749, 1227372988246171925067, 258975700519942276189137, 62413143825306088561582017, 17038788264308562177311890641
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..17.
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.
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=prod(k=1, n, k^2-k+1) \\ Charles R Greathouse IV, Mar 04 2012
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang May 04 2007, Jun 04 2010
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STATUS
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approved
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