A147630 a(1) = 1; for n>1, a(n) = Product_{k = 1..n-1} (9k - 3).

1, 6, 90, 2160, 71280, 2993760, 152681760, 9160905600, 632102486400, 49303993939200, 4289447472710400, 411786957380198400, 43237630524920832000, 4929089879840974848000, 606278055220439906304000, 80028703289098067632128000, 11284047163762827536130048000

Offset

1,2

Comments

Original name was: 9-factorial numbers (5).

Links

Table of n, a(n) for n=1..17.

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

Cf. A147629, A049211, A051232, A045756, A035012, A035013, A035017, A035018, A035020, A035022, A035023, A053116.

Cf. A048994, A097188, A132393.

Sequence in context: A266734 A004996 A001499 * A221097 A177584 A177558

Adjacent sequences: A147627 A147628 A147629 * A147631 A147632 A147633

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