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A084949 a(n) = Product_{i=0..n-1} (9*i+2).

%I A084949 #40 Aug 30 2025 02:43:44
%S A084949 1,2,22,440,12760,484880,22789360,1276204160,82953270400,
%T A084949 6138542009600,509498986796800,46873906785305600,4734264585315865600,
%U A084949 520769104384745216000,61971523421784680704000,7932354997988439130112000,1086732634724416160825344000,158662964669764759480500224000
%N A084949 a(n) = Product_{i=0..n-1} (9*i+2).
%H A084949 Robert Israel, <a href="/A084949/b084949.txt">Table of n, a(n) for n = 0..329</a>
%F A084949 a(n) = A084944(n)/A000142(n)*A000079(n) = 9^n*Pochhammer(2/9, n) = 9^n*Gamma(n+2/9)/Gamma(2/9).
%F A084949 a(n) = (-7)^n*Sum_{k=0..n} (9/7)^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 A084949 E.g.f.: (1-9*x)^(-2/9). - _Robert Israel_, Mar 22 2017
%F A084949 D-finite with recurrence: a(n) + (-9*n+7)*a(n-1) = 0. - _R. J. Mathar_, Jan 20 2020
%F A084949 Sum_{n>=0} 1/a(n) = 1 + (e/9^7)^(1/9)*(Gamma(2/9) - Gamma(2/9, 1/9)). - _Amiram Eldar_, Dec 21 2022
%F A084949 a(n) ~ sqrt(2*Pi) * (9/e)^n * n^(n-5/18) / Gamma(2/9). - _Amiram Eldar_, Aug 30 2025
%p A084949 a:= n-> product(9*i+2,i=0..n-1); seq(a(j),j=0..20);
%t A084949 Table[9^n*Pochhammer[2/9, n], {n,0,20}] (* _G. C. Greubel_, Aug 19 2019 *)
%o A084949 (PARI) vector(20, n, n--; prod(k=0, n-1, 9*k+2)) \\ _G. C. Greubel_, Aug 19 2019
%o A084949 (Magma) [1] cat [(&*[9*k+2: k in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Aug 19 2019
%o A084949 (Sage) [product(9*k+2 for k in (0..n-1)) for n in (0..20)] # _G. C. Greubel_, Aug 19 2019
%o A084949 (GAP) List([0..20], n-> Product([0..n-1], k-> 9*k+2) ); # _G. C. Greubel_, Aug 19 2019
%Y A084949 Cf. A000165, A008544, A001813, A047055, A047657, A084947, A084948.
%Y A084949 Cf. A000079, A000142, A035012, A048994, A084944.
%K A084949 easy,nonn,changed
%O A084949 0,2
%A A084949 Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003