|
| |
|
|
A025035
|
|
Number of partitions of { 1, 2, ..., 3n } into sets of size 3.
|
|
16
| |
|
|
1, 1, 10, 280, 15400, 1401400, 190590400, 36212176000, 9161680528000, 2977546171600000, 1208883745669600000, 599606337852121600000, 356765771022012352000000, 250806337028474683456000000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| P. Di Francesco, M. Gaudin, C. Itzykson and F. Lesage, Laughlin's wave functions, Coulomb gases and expansions of the discriminant, Int. J. Mod. Phys. A9 (1994) 4257. [From Paul Barry (pbarry(AT)wit.ie), Sep 02 2010]
B.G. Wybourne, Admissible partitions and the square of the Vandermonde determinant, 2003. [From Paul Barry (pbarry(AT)wit.ie), Sep 02 2010]
|
|
|
FORMULA
| (3n)!/(n!(3!)^n). (Christian G. Bower bowerc(AT)usa.net 9/1998).
Integral representation as n-th moment of a positive function on the positive axis, in Maple notation: int(x^n*sqrt(2/(3*x))*BesselK(1/3, 2*sqrt(2*x)/3)/Pi, x=0..infinity), n=0, 1... . Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 05 2005.
E.g.f.: exp(x^3/3!) (with interpolated zeros) - Paul Barry (pbarry(AT)wit.ie), May 26 2003
product( binomial(3*n-3*i,3) , i=0..n-1) / n! (equivalent to Christian Bower formula) - Olivier Gérard (olivier.gerard(AT)gmail.com, Feb 14 2011.
|
|
|
MATHEMATICA
| Select[Range[0, 39]! CoefficientList[Series[Exp[x^3/3!], {x, 0, 39}], x], # > 0 &] (* Geoffrey Critzer, Sep 24 2011 *)
|
|
|
PROG
| (PARI) {a(n) = if( n<0, 0, (3*n)! / n! / 6^n)} /* Michael Somos Mar 26 2003 */
(PARI) {a(n) = if( n<0, 0, prod( i=0, n-1, binomial( 3*n - 3*i, 3)) / n!)} /* Michael Somos Feb 15 2011 */
|
|
|
CROSSREFS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
Equals row sums of A157703
(End)
Sequence in context: A157713 A205824 A165457 * A012243 A186270 A077281
Adjacent sequences: A025032 A025033 A025034 * A025036 A025037 A025038
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
|
| |
|
|
