A084949 - OEIS

%I #35 Dec 21 2022 04:46:15

%S 1,2,22,440,12760,484880,22789360,1276204160,82953270400,

%T 6138542009600,509498986796800,46873906785305600,4734264585315865600,

%U 520769104384745216000,61971523421784680704000,7932354997988439130112000,1086732634724416160825344000,158662964669764759480500224000

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

%H Robert Israel, <a href="/A084949/b084949.txt">Table of n, a(n) for n = 0..329</a>

%F a(n) = A084944(n)/A000142(n)*A000079(n) = 9^n*Pochhammer(2/9, n) = 9^n*Gamma(n+2/9)/Gamma(2/9).

%F 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 E.g.f.: (1-9*x)^(-2/9). - _Robert Israel_, Mar 22 2017

%F D-finite with recurrence: a(n) +(-9*n+7)*a(n-1)=0. - _R. J. Mathar_, Jan 20 2020

%F 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

%p a:= n-> product(9*i+2,i=0..n-1); seq(a(j),j=0..20);

%t Table[9^n*Pochhammer[2/9, n], {n,0,20}] (* _G. C. Greubel_, Aug 19 2019 *)

%o (PARI) vector(20, n, n--; prod(k=0, n-1, 9*k+2)) \\ _G. C. Greubel_, Aug 19 2019

%o (Magma) [1] cat [(&*[9*k+2: k in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Aug 19 2019

%o (Sage) [product(9*k+2 for k in (0..n-1)) for n in (0..20)] # _G. C. Greubel_, Aug 19 2019

%o (GAP) List([0..20], n-> Product([0..n-1], k-> 9*k+2) ); # _G. C. Greubel_, Aug 19 2019

%Y Cf. A000165, A008544, A001813, A047055, A047657, A084947, A084948.

%Y Cf. A000079, A000142, A035012, A048994, A084944.

%K easy,nonn

%O 0,2

%A Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003