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A203473
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a(n) = v(n+1)/v(n), where v=A203472.
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4
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7, 72, 990, 17160, 360360, 8910720, 253955520, 8204716800, 296541907200, 11861676288000, 520431047136000, 24858235898496000, 1284342188088960000, 71382386874839040000, 4247252019052922880000
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OFFSET
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1,1
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LINKS
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FORMULA
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Since v(n) = (135/4)*(2^(n+2)^2/Pi^(n/2))*(BarnesG(n+3)*BarnesG(n+7/2) )/( BarnesG(9/2)*BarnesG(n+6) ) then v(n+1)/v(n) = Gamma(2*n+6) / Gamma(n+6). - G. C. Greubel, Aug 27 2023
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MATHEMATICA
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(* First program *)
f[j_]:= j+2; z=16;
v[n_]:= Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}];
d[n_]:= Product[(i-1)!, {i, n}] (* A000178 *)
Table[v[n+1]/v[n], {n, z-1}] (* this sequence *)
Table[v[n]/d[n], {n, 20}] (* A203474 *)
(* Second program *)
Table[Pochhammer[n+6, n], {n, 20}] (* G. C. Greubel, Aug 27 2023 *)
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PROG
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(Magma) [Floor(Gamma(2*n+6)/Gamma(n+6)): n in [1..16]]; // G. C. Greubel, Aug 27 2023
(SageMath) [rising_factorial(n+6, n) for n in range(1, 16)] # G. C. Greubel, Aug 27 2023
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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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