login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108400 a(n) = Product_{k = 0..n} k!*2^k. 9
1, 2, 16, 768, 294912, 1132462080, 52183852646400, 33664847019245568000, 347485857744891213250560000, 64560982045934655213753964953600000, 239901585047846581083822477336190648320000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform (see A001906 for definition) of the sequences A000898, A001861, A035009(with first term omitted), A047974, A067147(unsigned version), A083886.

Hankel transform of the sequence with e.g.f. exp(x^2). Also (-1)^C(n+1,2)*A108400(n) is the Hankel transform of the sequence with e.g.f. exp(-x^2). - Paul Barry, Feb 12 2008

Let T(n,k)=(n+1)^(k)(1+(-1)^(n-k))/2. Then a(n)=det(T(i,j);0<=i,j<=n). - Paul Barry, Feb 12 2008

LINKS

Table of n, a(n) for n=0..10.

M. E. Larsen, Wronskian Harmony, Mathematics Magazine, vol. 63, no. 1, 1990, pp. 33-37.

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

FORMULA

a(n) = A006125(n+1)*A000178(n).

a(n) = product{i=1..n, product{j=0..i-1, 2i-2j}}. - Paul Barry, Aug 02 2008

a(n) ~ 2^((n+1)^2/2) * n^(n^2/2+n+5/12) * Pi^((n+1)/2) / (A * exp(3*n^2/4+n-1/12)), where A = 1.2824271291... is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Nov 14 2014

MATHEMATICA

Table[Product[k!*2^k, {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 14 2014 *)

CROSSREFS

Cf. A000178, A006125, A074962.

Sequence in context: A278087 A015188 A005118 * A186002 A013029 A012915

Adjacent sequences:  A108397 A108398 A108399 * A108401 A108402 A108403

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jul 02 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 06:34 EST 2020. Contains 331033 sequences. (Running on oeis4.)