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 A130744 #38 May 17 2022 03:43:23
%S A130744 0,3,16,90,576,4200,34560,317520,3225600,35925120,435456000,
%T A130744 5708102400,80472268800,1214269056000,19527937228800,333456963840000,
%U A130744 6025763487744000,114887039275008000,2304854534062080000
%N A130744 a(n) = n*(n+2)*n!.
%C A130744 For n >= 1, a(n) = number whose factorial base representation (A007623) begins with a double digit {n}{n}, which is followed by n-1 zeros. Viewed in that base, this sequence looks like this: 0, 11, 220, 3300, 44000, 550000, 6600000, 77000000, 880000000, 9900000000, AA000000000, BB0000000000, ... (where "digits" A and B stand for placeholder values 10 and 11 respectively). - _Antti Karttunen_, May 07 2015
%H A130744 Vincenzo Librandi, <a href="/A130744/b130744.txt">Table of n, a(n) for n = 0..300</a>
%H A130744 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F A130744 0 = +a(n) * (+a(n+1) + 2*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+1) * (+5*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+2) * (+3*a(n+2) - a(n+4)) + a(n+3) * (+a(n+3)) if n>=0. - _Michael Somos_, Mar 26 2014
%F A130744 From _Antti Karttunen_, May 07 2015: (Start)
%F A130744 a(n) = n * (n! + (n+1)!) = n * A001048(n+1).
%F A130744 a(n) = A005563(n) * A000142(n).
%F A130744 a(n) = (n+2)! - (n+1)! - n! [from Orlovsky's Mathematica-code].
%F A130744 (End)
%F A130744 From _Amiram Eldar_, May 17 2022: (Start)
%F A130744 Sum_{n>=1} 1/a(n) = (Ei(1) - gamma)/2 - 1/4, where Ei(1) = A091725 and gamma = A001620.
%F A130744 Sum_{n>=1} (-1)^(n+1)/a(n) = (gamma - Ei(-1))/2 - 1/e + 1/4, where Ei(-1) = -A099285 and e = A001113. (End)
%e A130744 G.f. = 3*x + 16*x^2 + 90*x^3 + 576*x^4 + 4200*x^5 + 34560*x^6 + ...
%t A130744 a[n_]:=(n+2)!-(n+1)!-n!; (* _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008 *)
%o A130744 (Magma) [n*(n+2)*Factorial(n): n in [0..25]]; // _Vincenzo Librandi_, Aug 11 2011
%o A130744 (PARI) a(n)=n!*(n*(n+2)) \\ _Charles R Greathouse IV_, Aug 11 2011
%o A130744 (Scheme) (define (A130744 n) (* n (+ 2 n) (A000142 n))) ;; _Antti Karttunen_, May 07 2015
%Y A130744 Cf. A000142, A001048, A005563, A007623.
%Y A130744 Column 3 of A257503 (apart from initial zero. Equally, row 3 of A257505).
%Y A130744 Subsequence of both A227130 and A227148.
%Y A130744 Cf. A001113, A001620, A091725, A099285.
%K A130744 nonn,easy
%O A130744 0,2
%A A130744 _Paul Curtz_, Jul 12 2007
%E A130744 More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008