0,2

Also a(n)=(((n)!)^2)*A006480.

Harry J. Smith, Table of n, a(n) for n=0,...,70

K. A. Penson and A. I. Solomon, Coherent states from combinatorial sequences.

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

(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]

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: A059415 A002684 A036281 this_sequence A069945 A086205 A042759

Adjacent sequences: A064347 A064348 A064349 this_sequence A064351 A064352 A064353

nonn

Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 18 2001

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