A154604 Hankel transform of reduced tangent numbers.

1, 1, 3, 54, 9720, 26244000, 1488034800000, 2362404048480000000, 135019896025206528000000000, 347259290825980971841536000000000000, 49121618545275670528799969525760000000000000000

Offset

0,3

Comments

Hankel transform of A002105 (with interpolated zeros).

Hankel transform of A154603.

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

Cf. A002105, A154603.

Sequence in context: A157568 A156911 A214006 * A188798 A334248 A193256

Adjacent sequences: A154601 A154602 A154603 * A154605 A154606 A154607

Keyword

easy,nonn

Author

Paul Barry, Jan 12 2009

Status

approved