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1, 2, 15, 252, 7560, 356400, 24324300, 2270268000, 277880803200, 43197833952000, 8315583035760000, 1942008468966720000, 540988073497872000000, 177227692877902867200000, 67457290601651778828000000, 29522484828017013792960000000, 14721879100904484211422720000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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a(n) ~ sqrt(Pi) * 2^(n+3) * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Jan 25 2019
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MAPLE
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b:= proc(n) option remember; uses LinearAlgebra;
Determinant(VandermondeMatrix([i*(i+1)/2$i=1..n]))
end:
a:= n-> b(n+1)/b(n):
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MATHEMATICA
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(* First program *)
f[j_]:= j*(j+1)/2; z = 15;
v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}]
Table[v[n+1]/v[n], {n, 0, z-1}] (* A203310 *)
(* Second program *)
Table[(n!*(2*n+2)!)/(2^n*(n+2)!), {n, 0, 20}] (* G. C. Greubel, Aug 29 2023 *)
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PROG
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(Python)
from operator import mul
from functools import reduce
def f(n): return n*(n + 1)//2
def v(n): return 1 if n==1 else reduce(mul, (f(k) - f(j) for k in range(2, n + 1) for j in range(1, k)))
print([v(n + 1)//v(n) for n in range(1, 15)]) # Indranil Ghosh, Jul 24 2017
(Magma) F:= Factorial; [(F(n)*F(2*n+2))/(2^n*F(n+2)): n in [0..20]]; // G. C. Greubel, Aug 29 2023
(SageMath) f=factorial; [(f(n)*f(2*n+2))/(2^n*f(n+2)) for n in range(21)] # G. C. Greubel, Aug 29 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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EXTENSIONS
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STATUS
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approved
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