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

%I A147630 #55 Nov 03 2024 09:33:43
%S A147630 1,6,90,2160,71280,2993760,152681760,9160905600,632102486400,
%T A147630 49303993939200,4289447472710400,411786957380198400,
%U A147630 43237630524920832000,4929089879840974848000,606278055220439906304000,80028703289098067632128000,11284047163762827536130048000
%N A147630 a(1) = 1; for n>1, a(n) = Product_{k = 1..n-1} (9k - 3).
%C A147630 Original name was: 9-factorial numbers (5).
%F A147630 a(n+1) = Sum_{k, 0<=k<=n}A132393(n,k)*6^k*9^(n-k). - _Philippe Deléham_, Nov 09 2008
%F A147630 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 for n>1, also a(n) = n!*A097188(n-1). - _Vladimir Kruchinin_, Apr 01 2011
%F A147630 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
%F A147630 a(n) = round(9^n * Gamma(n+6/9) / Gamma(6/9)). - _Vincenzo Librandi_, Feb 21 2015
%F A147630 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
%t A147630 s=1;lst={s};Do[s+=n*s;AppendTo[lst,s],{n,5,2*5!,9}];lst
%t A147630 Table[Product[9k-3,{k,1,n-1}],{n,20}] (* _Harvey P. Dale_, Sep 01 2016 *)
%o A147630 (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 */
%o A147630 (Magma) [Round(9^n*Gamma(n+6/9)/Gamma(6/9)): n in [0..20]]; // _Vincenzo Librandi_, Feb 21 2015
%o A147630 (PARI) a(n) = n--; prod(k=1, n, 9*k-3); \\ _Michel Marcus_, Feb 28 2015
%Y A147630 Cf. A147629, A049211, A051232, A045756, A035012, A035013, A035017, A035018, A035020, A035022, A035023, A053116.
%Y A147630 Cf. A048994, A097188, A132393.
%K A147630 nonn,easy
%O A147630 1,2
%A A147630 _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008
%E A147630 New name from _Peter Bala_, Feb 20 2015
%E A147630 More terms from _Michel Marcus_, Feb 28 2015