This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A144758 #30 Mar 09 2025 11:37:43
%S A144758 1,3,36,756,22680,884520,42456960,2420046720,159723083520,
%T A144758 11979231264000,1006255426176000,93581754634368000,
%U A144758 9545338972705536000,1059532625970314496000,127143915116437739520000,16401565050020468398080000,2263415976902824638935040000
%N A144758 Partial products of successive terms of A017197.
%H A144758 G. C. Greubel, <a href="/A144758/b144758.txt">Table of n, a(n) for n = 0..250</a>
%F A144758 a(n) = Sum_{k=0..n} A132393(n,k)*3^k*9^(n-k).
%F A144758 a(n) = (-6)^n*Sum_{k=0..n} (3/2)^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 A144758 Sum_{n>=0} 1/a(n) = 1 + (e/9^6)^(1/9)*(Gamma(1/3) - Gamma(1/3, 1/9)). - _Amiram Eldar_, Dec 21 2022
%e A144758 a(0)=1, a(1)=3, a(2)=3*12=36, a(3)=3*12*21=756, a(4)=3*12*21*30=22680, ...
%p A144758 seq(9^n*pochhammer(1/3, n), n = 0..20); # _G. C. Greubel_, Dec 03 2019
%t A144758 Table[9^n*Pochhammer[1/3, n], {n, 0, 20}] (* _G. C. Greubel_, Dec 03 2019 *)
%t A144758 Join[{1},FoldList[Times,NestList[#+9&,3,20]]] (* _Harvey P. Dale_, Mar 09 2025 *)
%o A144758 (PARI) a(n)=3^n*prod(i=1,n,3*i-2) \\ _Charles R Greathouse IV_, Jan 17 2012
%o A144758 (Magma) [Round(9^n*Gamma(n+1/3)/Gamma(1/3)): n in [0..20]]; // _G. C. Greubel_, Dec 03 2019
%o A144758 (Sage) [9^n*rising_factorial(1/3, n) for n in (0..20)] # _G. C. Greubel_, Dec 03 2019
%Y A144758 Cf. A048994, A132393.
%Y A144758 Cf. A001710, A001147, A008545, A011781, A032031, A047056, A144739, A144756.
%K A144758 nonn,easy
%O A144758 0,2
%A A144758 _Philippe Deléham_, Sep 20 2008