A091804 a(n) = 2^(n*(n+1)/2)*A055209(n).

1, 2, 32, 9216, 84934656, 39137889484800, 1298501242170900480000, 4221953171600428240994304000000, 1757091687362157576297527910177177600000000

Offset: 0

Author

Philippe Deléham, Mar 07 2004

Keywords

• nonn

Comments

This sequence is the Hankel transform (see A001906 for definition) of A000629, A000670 (Fubini numbers) and A052841.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..30
• P. Barry, Eulerian Polynomials as Moments, via Exponential Riordan Arrays, J. Int. Seq. 14 (2011) # 11.9.5.
• P. 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]

Crossrefs

Cf. A000629, A000670, A001906, A052841, A055209.

Programs

Magma

[(&*[(2*(k+1)*Floor((2*k+3)/2))^(n-k): k in [0..n]]): n in [0..10]]; // G. C. Greubel, Oct 14 2018

Mathematica

Table[Product[(2(k+1)Floor[(2k+3)/2])^(n-k),{k,0,n}],{n,0,10}] (* Harvey P. Dale, Aug 10 2011 *)

PARI

for(n=0,10, print1(prod(k=0,n, (2*(k+1)*floor((2*k+3)/2))^(n-k)), ", ")) \\ G. C. Greubel, Oct 14 2018

Formula

a(n) = Product{k=0..n} (2(k+1)*floor((2k+3)/2))^(n-k). - Paul Barry, Mar 30 2010