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A113895
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a(n) = C(2+2*n, n) * C(7+2*n, 2+n).
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1
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21, 336, 4950, 72072, 1051050, 15402816, 226972746, 3362559200, 50062040028, 748664904000, 11241203533560, 169398104243760, 2561053271692500, 38833447762771200, 590405728218941250, 8998028449224091200, 137437148161776305700, 2103486475191421320000, 32253916565936980114200
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = C(2+2*n, n) * C(7+2*n, 2+n).
24*(11+2*n)*(5+2*n)*(n+3)*a(n+1)-2*(n+4)*(11*n^2+112*n+252)*a(n+2)+(8+n)*(n+5)*(n+3)*a(n+3)=0. (End)
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EXAMPLE
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if n=0 then C(2+2*0,0)*C(7+2*0,2+0)=C(2,0)*C(7,2)=1*21=21;
if n=7 then C(2+2*7,7)*C(7+2*7,2+7)=C(16,7)*C(21,9)=11440*293930=3362559200;
if n=10 then C(2+2*10,10)*C(7+2*10,2+10)=C(22,10)*C(27,12)=646646*17383860=11241203533560.
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MAPLE
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seq(binomial(2+2*n, n)*binomial(7+2*n, 2+n), n=0..20); # Robert Israel, Dec 16 2018
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MATHEMATICA
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nmax = 10; NN[5, m_, x_] := x^m*(2*m+5)!*Hypergeometric2F1[-m, -m, -2*m-5, (x-1)/x]/((m+5)!*m!); tri = Table[CoefficientList[NN[5, m, x], x], {m, 0, 2*nmax+2}]; Table[tri[[2n+3, n+3]], {n, 0, nmax}] (* Jean-François Alcover, Sep 18 2013 *)
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PROG
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(PARI) a(n) = binomial(2+2*n, n)*binomial(7+2*n, 2+n); \\ Michel Marcus, Sep 18 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Simpler name and more terms added by Joerg Arndt, Sep 18 2013
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STATUS
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approved
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