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 A107713 #20 Dec 07 2020 17:32:30
%S A107713 1,3,12,66,484,4536,52128,709776,11153376,198339840,3932962560,
%T A107713 85976743680,2053285148160,53173906652160,1483987541299200,
%U A107713 44396218792396800,1417294759310438400,48088097391133900800,1728013936221838540800,65558270633421791232000
%N A107713 Convolution of 2^n*n! and n!.
%C A107713 E.g.f. is int( 1/((1-t)(1-2*(x+t))), t=0..x).
%F A107713 a(n) = Sum_{k=0..n} 2^k * k! * (n-k)!.
%F A107713 E.g.f. (for offset 1): (log(1-x)+log(1-2*x))/(-3+2*x).
%F A107713 a(n) ~ n! * 2^n * (1 + 1/(2*n) + 1/(2*n^2) + 5/(4*n^3) + 17/(4*n^4) + 37/(2*n^5) + 98/n^6 + 4885/(8*n^7) + 34969/(8*n^8) + 70657/(2*n^9) + 636151/(2*n^10) + ...). - _Vaclav Kotesovec_, Aug 08 2019, extended Dec 07 2020
%e A107713 a(4) = 484 = 4! 0! + 2 3! 1! + 2^2 2! 2! + 2^3 1! 3! + 2^4 0! 4!
%p A107713 f:=proc(n) local k; add(2^k*k!*(n-k)!,k=0..n); end:
%t A107713 Rest[Range[0, 20]! CoefficientList[Series[((Log[1 - x] + Log[1 - 2 x]))/(-3 + 2 x), {x, 0, 20}], x]] (* _Vincenzo Librandi_, Jul 13 2015 *)
%t A107713 Table[Sum[2^k * k! * (n-k)!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Aug 08 2019 *)
%Y A107713 Cf. A003149, A108953, A110467.
%K A107713 nonn
%O A107713 0,2
%A A107713 _Mike Zabrocki_, Jun 10 2005