OFFSET
0,3
LINKS
Paul Barry, A Note on d-Hankel Transforms, Continued Fractions, and Riordan Arrays, arXiv:1702.04011 [math.CO], 2017.
FORMULA
a(n) = Prod_{k=0..n} ((k+2)*(k+1)^2)^(floor((n-k)/2)).
a(n) ~ 2^(3*n/4 + (5 + (-1)^n)/8) * Pi^(3*n/4 + (5 - (-1)^n)/8) * n^(3*n^2/4 + 5*n/4 + 3/8) / (A^(3/2) * exp(9*n^2/8 + 5*n/4 - 1/8)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jan 23 2024
MATHEMATICA
f[n_]:=Product[((k + 2) (k + 1)^2)^(Floor[(n - k) / 2]), {k, 0, n}]; Table[f[n], {n, 0, 12}] (* Vincenzo Librandi, Sep 26 2017 *)
PROG
(Magma) [&*[((k+2)*(k+1)^2)^(Floor((n-k)/2)): k in [0..n]]: n in [0..16]]; // Vincenzo Librandi, Sep 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Sep 23 2017
STATUS
approved