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 A317618 #18 Jan 30 2020 21:29:18
%S A317618 1,1,5,39,417,5685,94365,1847475,41686785,1065288105,30411314325,
%T A317618 959236098975,33129890726625,1243507150410525,50401090111697325,
%U A317618 2193907232242600875,102075654396429338625,5055304328553234380625,265522264682686831945125,14742355948224269570580375
%N A317618 Expansion of e.g.f. sqrt((1 - x)/(1 - 3*x)).
%C A317618 Lah transform of A001147.
%H A317618 Robert Israel, <a href="/A317618/b317618.txt">Table of n, a(n) for n = 0..380</a>
%H A317618 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A317618 a(n) = Sum_{k=0..n} binomial(n-1,k-1)*(2*k-1)!!*n!/k!.
%F A317618 a(n) ~ 2 * 3^(n - 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Mar 26 2019
%F A317618 D-finite with recurrence: (3*n^2 + 3*n)*a(n) + (-5 - 4*n)*a(n + 1) + a(n + 2)=0. - _Robert Israel_, Mar 26 2019
%p A317618 a:=series(sqrt((1 - x)/(1 - 3*x)), x=0, 20): seq(n!*coeff(a, x, n), n=0..19); # _Paolo P. Lava_, Mar 26 2019
%t A317618 nmax = 19; CoefficientList[Series[Sqrt[(1 - x)/(1 - 3*x)], {x, 0, nmax}], x] Range[0, nmax]!
%t A317618 Table[Sum[Binomial[n - 1, k - 1] (2 k - 1)!! n!/k!, {k, 0, n}], {n, 0, 19}]
%t A317618 Join[{1}, Table[n! Hypergeometric2F1[3/2, 1 - n, 2, -2], {n, 19}]]
%o A317618 (PARI) my(x='x + O('x^25)); Vec(serlaplace(sqrt((1 - x)/(1 - 3*x)))) \\ _Michel Marcus_, Mar 26 2019
%Y A317618 Cf. A000246, A001147, A002866, A052563, A084262.
%K A317618 nonn
%O A317618 0,3
%A A317618 _Ilya Gutkovskiy_, Aug 01 2018