OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..34
Paul Barry, A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences, Journal of Integer Sequences, Vol. 15 (2012), #12.7.2. - N. J. A. Sloane, Dec 27 2012
FORMULA
a(n) = Product_{k=1..n} C(k+1,2)^(n-k+1).
a(n) ~ n^(n^2 + 3*n + 7/3) * Pi^(n + 3/2) / (A^2 * 2^((n^2 - n - 3)/2) * exp(3*n^2/2 + 3*n - 1/6)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Nov 13 2022
MATHEMATICA
Table[Product[(k*(k+1)/2)^(n - k + 1), {k, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Nov 13 2022 *)
PROG
(PARI) a(n) = prod(k=1, n, binomial(k+1, 2)^(n-k+1)); \\ Michel Marcus, Nov 13 2022
(Magma) [n eq 0 select 1 else (&*[(Binomial(k+1, 2))^(n-k+1): k in [1..n]]): n in [0..15]]; // G. C. Greubel, May 30 2024
(SageMath) [product((binomial(k+1, 2))^(n-k+1) for k in range(1, n+1)) for n in range(16)] # G. C. Greubel, May 30 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 12 2009
STATUS
approved