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A133351
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Dimensions of certain Lie algebra (see reference for precise definition).
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1
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1, 189, 6720, 103125, 945945, 6117748, 30707712, 127152180, 452615625, 1426106605, 4063625280, 10643113845, 25946898705, 59468850000, 129170145280, 267637365072, 531858496113, 1018308094245, 1885647400000, 3388127079645, 5923761615849, 10102561208916
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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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Empirical g.f.: -(x +1)*(x^8 +175*x^7 +4166*x^6 +26055*x^5 +50086*x^4 +26055*x^3 +4166*x^2 +175*x +1) / (x -1)^13. - Colin Barker, Jul 27 2013
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MAPLE
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b:=binomial; t72c:= proc(a, k) ((4*k+3*a+2)/((3*a+2)*(k+1))) * b(k+a, k)*b(k+a+1, k)*b(k+3*a/2-1, k)*b(k+3*a/2, k)*b(2*k+2*a+1, 2*k)/ (b(k+a/2-1, k)*b(k+a/2, k)*b(2*k+a, 2*k)); end; [seq(t72c(2, k), k=0..40)];
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MATHEMATICA
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t72c[a_, k_] := (4k+3a+2) / ((k+1)(3a+2)) Binomial[k+a, k] Binomial[k+a+1, k] Binomial[k+3/2a-1, k] Binomial[k+3/2a, k] Binomial[2k+2a+1, 2k] / (Binomial[k+a/2-1, k] Binomial[k+a/2, k] Binomial[2k+a, 2k]);
Array[t72c[2, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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