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

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

Offset

0,2

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]

Formula

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A129349 A180127 A342099 * A012853 A128146 A185995

Adjacent sequences: A091801 A091802 A091803 * A091805 A091806 A091807

Keyword

nonn

Author

Philippe Deléham, Mar 07 2004

Status

approved