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A147585 a(1) = 1; a(n) = (7*n-9)*a(n-1) for n > 1.

%I A147585 #31 Dec 19 2022 03:43:05
%S A147585 1,5,60,1140,29640,978120,39124800,1838865600,99298742400,
%T A147585 6057223286400,411891183475200,30891838760640000,2533130778372480000,
%U A147585 225448639275150720000,21643069370414469120000,2229236145152690319360000,245215975966795935129600000,28690269188115124410163200000
%N A147585 a(1) = 1; a(n) = (7*n-9)*a(n-1) for n > 1.
%H A147585 G. C. Greubel, <a href="/A147585/b147585.txt">Table of n, a(n) for n = 1..340</a>
%F A147585 a(n) = Product_{k=1..n-1} (7*k - 2). - _Klaus Brockhaus_, Nov 10 2008
%F A147585 a(n) = (5*7^(n-1)*Gamma(5/7+n))/Gamma(12/7). - _Klaus Brockhaus_, Nov 10 2008
%F A147585 a(n+1) = Sum_{k=0..n} A132393(n,k)*5^k*7^(n-k). - _Philippe Deléham_, Nov 09 2008
%F A147585 G.f.: x/(1-5x/(1-7x/(1-12x/(1-14x/(1-19x/(1-21x/(1-26x/(1-... (continued fraction). - _Philippe Deléham_, Jan 08 2012
%F A147585 a(n) = (-2)^n*Sum_{k=0..n} (7/2)^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 A147585 Sum_{n>=1} 1/a(n) = 1 + (e/7^2)^(1/7)*(Gamma(5/7) - Gamma(5/7, 1/7)). - _Amiram Eldar_, Dec 19 2022
%p A147585 seq( -7^n*pochhammer(-2/7, n)/2, n = 1..15); # _G. C. Greubel_, Dec 03 2019
%t A147585 Table[-7^n*Pochhammer[-2/7, n]/2, {n, 15}] (* _G. C. Greubel_, Dec 03 2019 *)
%o A147585 (Magma) [ n eq 1 select 1 else Self(n-1)*(7*n-9): n in [1..15] ]; // _Klaus Brockhaus_, Nov 10 2008
%o A147585 (Magma) [ 1 ] cat [ &*[ (5+7*k): k in [0..n-1] ]: n in [1..14] ]; // _Klaus Brockhaus_, Nov 10 2008
%o A147585 (PARI) {for(n=1, 15, print1(prod(k=1, n-1, 7*k-2,), ","))} \\ _Klaus Brockhaus_, Nov 10 2008
%o A147585 (Sage) [-7^n*rising_factorial(-2/7, n)/2 for n in (1..15)] # _G. C. Greubel_, Dec 03 2019
%Y A147585 Cf. A048994, A132393.
%Y A147585 Cf. A045754, A049209, A084947, A144739, A144827, A051188.
%K A147585 nonn
%O A147585 1,2
%A A147585 _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008
%E A147585 Edited by _Klaus Brockhaus_, Nov 10 2008