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A062149
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Third column sequence of triangle A062138 (generalized a=5 Laguerre).
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3
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1, 24, 432, 7200, 118800, 1995840, 34594560, 622702080, 11675664000, 228324096000, 4657811558400, 99084354969600, 2196369868492800, 50685458503680000, 1216451004088320000, 30330178368602112000
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: (1 + 14*x + 21*x^2)/(1 - x)^10.
a(n) = (n+2)!*binomial(n+7, 7)/2!.
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j), then a(n-2) = (-1)^n*f(n,2,-8), (n >= 2). - Milan Janjic, Mar 01 2009
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EXAMPLE
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a(2) = (2+2)! * binomial(2+7,7) / 2! = (24 * 36) / 2 = 432. - Indranil Ghosh, Feb 24 2017
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MAPLE
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a:=n-> (n+2)!*binomial(n+7, 7)/2!: seq(a(n), n=0..22); # Zerinvary Lajos, Apr 29 2007
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MATHEMATICA
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Table[(n+2)!*Binomial[n+7, 7]/2!, {n, 0, 15}] (* Indranil Ghosh, Feb 24 2017 *)
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PROG
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(Python)
import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
(Magma) [Factorial(n+2)*Binomial(n+7, 7)/2: n in [0..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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