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A091804
a(n) = 2^(n*(n+1)/2)*A055209(n).
4
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
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
KEYWORD
nonn
AUTHOR
Philippe Deléham, Mar 07 2004
STATUS
approved