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A130563
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Fourth column (m=3) of the Laguerre-Sonin a=1/2 coefficient triangle.
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4
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1, 36, 990, 25740, 675675, 18378360, 523783260, 15713497800, 496939367925, 16564645597500, 581419060472250, 21459648959248500, 831561397170879375, 33774185977401870000, 1435402904039579475000, 63731888939357328690000
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OFFSET
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3,2
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LINKS
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FORMULA
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a(n) = n!*(2^(n-3))*binomial(n+1/2,n-3)/3!, n >= 3.
a(n) = binomial(n,3)*(2*n+1)!!/7!!, with (2*n+1)!! = A001147(n+1).
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MATHEMATICA
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Table[n!*(2^(n - 3))*Binomial[n + 1/2, n - 3]/3!, {n, 3, 50}] (* G. C. Greubel, May 12 2018 *)
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PROG
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(PARI) for(n=3, 20, print1(n!*(2^(n-3))*binomial(n+1/2, n-3)/3!, ", ")) \\ G. C. Greubel, May 12 2018
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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