OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..55
FORMULA
a(n) ~ 3*A^(3/2) * 2^(n^2 + 4*n + 185/24) * exp(n/2 - 1/8) / (Pi^(n/2 + 3/2) * n^(n/2 + 59/8)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 09 2021
From G. C. Greubel, Aug 27 2023: (Start)
a(n) = Product_{j=1..n} binomial(2*j+3, j+4).
a(n) = (18*2^(n+2)^2/Pi^(n/2))*BarnesG(n+3)*BarnesG(n+7/2)/( BarnesG(n +1)*BarnesG(n+6)*BarnesG(7/2)). (End)
MATHEMATICA
(* 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(n-1) *)
Table[v[n], {n, z}] (* A203472 *)
Table[v[n+1]/v[n], {n, z-1}] (* A203473 *)
Table[v[n]/d[n], {n, 20}] (* A203474 *)
(* Second program *)
Table[Product[Binomial[2*j+3, j+4], {j, n}], {n, 20}] (* G. C. Greubel, Aug 27 2023 *)
PROG
(Magma) [(&*[ Binomial(2*j+3, j+4): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 27 2023
(SageMath) [product( binomial(2*j+5, j+5) for j in range(n) ) for n in range(1, 20)] # G. C. Greubel, Aug 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 02 2012
EXTENSIONS
Definition corrected by Vaclav Kotesovec, Apr 09 2021
STATUS
approved