OFFSET
1,2
COMMENTS
Original name was: 9-factorial numbers (5).
FORMULA
a(n+1) = Sum_{k, 0<=k<=n}A132393(n,k)*6^k*9^(n-k). - Philippe Deléham, Nov 09 2008
a(n) = n!*sum(k=1..n-1, binomial(k,n-k-1)*3^k*(-1)^(n-k-1)*binomial(n+k-1,n-1)))/n, also a(n) = n!*A097188(n). - Vladimir Kruchinin, Apr 01 2011
a(n) = (-3)^n*sum_{k=0..n} 3^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = round(9^n * Gamma(n+6/9) / Gamma(6/9)). - Vincenzo Librandi, Feb 21 2015
Sum_{n>=1} 1/a(n) = 1 + (e/9^3)^(1/9)*(Gamma(2/3) - Gamma(2/3, 1/9)). - Amiram Eldar, Dec 21 2022
MATHEMATICA
s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 2*5!, 9}]; lst
Table[Product[9k-3, {k, 1, n-1}], {n, 20}] (* Harvey P. Dale, Sep 01 2016 *)
PROG
(Maxima) a(n):=n!*sum(binomial(k, n-k-1)*3^k*(-1)^(n-k-1)*binomial(n+k-1, n-1), k, 1, n-1))/n; /* Vladimir Kruchinin, Apr 01 2011 */
(Magma) [Round(9^n*Gamma(n+6/9)/Gamma(6/9)): n in [0..20]]; // Vincenzo Librandi, Feb 21 2015
(PARI) a(n) = n--; prod(k=1, n, 9*k-3); \\ Michel Marcus, Feb 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Nov 08 2008
EXTENSIONS
New name from Peter Bala, Feb 20 2015
More terms from Michel Marcus, Feb 28 2015
STATUS
approved