|
| |
| |
|
|
|
1, 6, 360, 60480, 19958400, 10897286400, 8892185702400, 10137091700736000, 15388105201717248000, 30006805143348633600000, 73096577329197271449600000, 217535414131691079834009600000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Also a(n)=(((n)!)^2)*A006480.
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,70
K. A. Penson and A. I. Solomon, Coherent states from combinatorial sequences.
|
|
|
FORMULA
| Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*BesselK(1/3, 2*sqrt(x/27))/(3*Pi*sqrt(x)), x=0..infinity), n=0, 1, ...
A recursive formula: a(i) = (27 * (i - 1)^2 + 27 * (i - 1) + 6) * a(i - 1) with a(0) = 1. An explicit formula following from the recursion equation: a(n) = (3/2)*27^n*GAMMA(n+2/3)*GAMMA(n+1/3)/(Pi*3^(1/2)). - Thomas Wieder (wieder.thomas(AT)t-online.de), Nov 15 2004
E.g.f.: (of aerated sequence) 2*cos(arcsin((3*sqrt(3)x/2)/3))/sqrt(4-27x^2). [From Paul Barry (pbarry(AT)wit.ie), Jul 27 2010]
|
|
|
PROG
| (PARI) { t=f=1; for (n=0, 70, if (n, t*=3*n*(3*n - 1)*(3*n - 2); f*=n); write("b064350.txt", n, " ", t/f) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 12 2009]
|
|
|
CROSSREFS
| Cf. A006480.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
Equals A001525*3!
Equals row sums of A157704 and A157705.
(End)
Sequence in context: A002684 A036281 A202367 * A069945 A086205 A173608
Adjacent sequences: A064347 A064348 A064349 * A064351 A064352 A064353
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 18 2001
|
|
|
EXTENSIONS
| The formula for a(n) and two links were corrected by Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 02 2009
a(11) from Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 12 2009
|
| |
|
|
