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 A153647 #24 May 31 2025 06:48:41
%S A153647 2,18,216,3240,58320,1224720,29393280,793618560,23808556800,
%T A153647 785682374400,28284565478400,1103098053657600,46330118253619200,
%U A153647 2084855321412864000,100073055427817472000,5103725826818691072000,275601194648209317888000,15709268094947931119616000
%N A153647 a(n) = 3^n*(n + 2)!.
%H A153647 G. C. Greubel, <a href="/A153647/b153647.txt">Table of n, a(n) for n = 0..300</a>
%F A153647 From _G. C. Greubel_, Mar 03 2021: (Start)
%F A153647 a(n) = 2*A051606(n).
%F A153647 G.f.: 2*Hypergeometric2F0([1, 3]; --; 3*x).
%F A153647 E.g.f.: 2/(1-3*x)^3. (End)
%F A153647 D-finite with recurrence a(n) + 3*(-n-2)*a(n-1) = 0. - _R. J. Mathar_, Aug 20 2021
%F A153647 From _Amiram Eldar_, May 31 2025: (Start)
%F A153647 Sum_{n>=0} 1/a(n) = 9*exp(1/3) - 12.
%F A153647 Sum_{n>=0} (-1)^n/a(n) = 9*exp(-1/3) - 6. (End)
%p A153647 A153647:= n-> 3^n*(n+2)!; seq(A153647(n), n=0..20); # _G. C. Greubel_, Mar 03 2021
%t A153647 Table[3^n*(n + 2)!, {n, 0, 30}]
%o A153647 (Magma) [3^n*Factorial(n + 2): n in [0..20]]; // _Vincenzo Librandi_, Aug 24 2016
%o A153647 (Sage) [3^n*factorial(n+2) for n in (0..20)] # _G. C. Greubel_, Mar 03 2021
%o A153647 (PARI) a(n) = 3^n*(n + 2)!; \\ _Michel Marcus_, Mar 03 2021
%Y A153647 Cf. A051606.
%K A153647 nonn,easy
%O A153647 0,1
%A A153647 _Roger L. Bagula_ and _Gary W. Adamson_, Dec 30 2008