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 A232688 #10 Mar 01 2024 02:05:14
%S A232688 1,1,6,24,160,1100,9168,84336,868544,9806688,120754080,1608251040,
%T A232688 23036978688,353070167424,5764504370688,99875064159360,
%U A232688 1830107743518720,35360088597841920,718450398365755392,15313427783968370688,341652563064038062080,7962756873168407869440
%N A232688 Expansion of 1/(1-x)^(1+2*x).
%C A232688 Generally, if E.g.f. = 1/(1-x)^(1+p*x) then a(n) ~ n! * n^p/p! * (1 - p^2*log(n)/n). - _Vaclav Kotesovec_, Nov 29 2013
%F A232688 E.g.f.: Sum_{n>=0} x^n/n! * Product_{k=1..n} (k + 2*x).
%F A232688 a(n) ~ n! * n^2/2 * (1-4*log(n)/n). - _Vaclav Kotesovec_, Nov 29 2013
%e A232688 E.g.f.: A(x) = 1 + x + 6*x^2/2! + 24*x^3/3! + 160*x^4/4! + 1100*x^5/5! + 9168*x^6/6! +...
%e A232688 where
%e A232688 A(x) = 1 + (1+2*x)*x + (1+2*x)*(2+2*x)*x^2/2! + (1+2*x)*(2+2*x)*(3+2*x)*x^3/3! + (1+2*x)*(2+2*x)*(3+2*x)*(4+2*x)*x^4/4! + (1+2*x)*(2+2*x)*(3+2*x)*(4+2*x)*(5+2*x)*x^5/5! +...
%t A232688 CoefficientList[Series[1/(1-x)^(1+2*x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 29 2013 *)
%o A232688 (PARI) {a(n)=n!*polcoeff(sum(m=0, n, prod(k=1, m, k+2*x)*x^m/m!)+x*O(x^n), n)}
%o A232688 for(n=0,30,print1(a(n),", "))
%o A232688 (PARI) {a(n)=n!*polcoeff((1-x+x*O(x^n))^(-1-2*x), n)}
%o A232688 for(n=0,30,print1(a(n),", "))
%Y A232688 Cf. A073479.
%K A232688 nonn
%O A232688 0,3
%A A232688 _Paul D. Hanna_, Nov 27 2013