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%I #14 Sep 08 2022 08:45:30
%S 1,36,990,25740,675675,18378360,523783260,15713497800,496939367925,
%T 16564645597500,581419060472250,21459648959248500,831561397170879375,
%U 33774185977401870000,1435402904039579475000,63731888939357328690000
%N Fourth column (m=3) of the Laguerre-Sonin a=1/2 coefficient triangle.
%H G. C. Greubel, <a href="/A130563/b130563.txt">Table of n, a(n) for n = 3..400</a>
%F a(n) = n!*(2^(n-3))*binomial(n+1/2,n-3)/3!, n >= 3.
%F a(n) = binomial(n,3)*(2*n+1)!!/7!!, with (2*n+1)!! = A001147(n+1).
%F a(n) = -A130757(n,3), n >= 3.
%t Table[n!*(2^(n - 3))*Binomial[n + 1/2, n - 3]/3!, {n, 3, 50}] (* _G. C. Greubel_, May 12 2018 *)
%o (PARI) for(n=3, 20, print1(n!*(2^(n-3))*binomial(n+1/2, n-3)/3!, ", ")) \\ _G. C. Greubel_, May 12 2018
%o (Magma) [Round(Factorial(n)*2^(n-3)*Gamma(n+3/2)/(6*Gamma(n-2)*Gamma(9/2))): n in [3..20]]; // _G. C. Greubel_, May 12 2018
%Y Columns m=0, 1, 2 from A001147, A000457, A001881.
%Y Eighth right hand column of triangle A001498. - _Johannes W. Meijer_, Oct 16 2009
%K nonn,easy
%O 3,2
%A _Wolfdieter Lang_, Jul 13 2007
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