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 A203310 a(n) = A203309(n+1)/A203309(n). 3
 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)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..200 FORMULA a(n) ~ sqrt(Pi) * 2^(n+3) * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Jan 25 2019 a(n) = (n!*(2*n+2)!)/(2^n*(n+2)!). - G. C. Greubel, Aug 29 2023 MAPLE b:= proc(n) option remember; uses LinearAlgebra; Determinant(VandermondeMatrix([i*(i+1)/2\$i=1..n])) end: a:= n-> b(n+1)/b(n): seq(a(n), n=0..16); # Alois P. Heinz, Aug 29 2023 MATHEMATICA (* 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], {n, z}] (* A203309 *) 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 *) PROG (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 CROSSREFS Cf. A203306, A203309. Sequence in context: A156750 A292798 A221100 * A102555 A264907 A195737 Adjacent sequences: A203307 A203308 A203309 * A203311 A203312 A203313 KEYWORD nonn AUTHOR Clark Kimberling, Jan 01 2012 EXTENSIONS Name corrected by Vaclav Kotesovec, Jan 25 2019 a(0)=1 prepended by Alois P. Heinz, Aug 29 2023 STATUS approved

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Last modified September 22 09:12 EDT 2023. Contains 365520 sequences. (Running on oeis4.)