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 A309618 #8 Aug 10 2019 09:31:55
%S A309618 1,1,4,8,36,140,832,5376,42432,374592,3720960,40694784,486679296,
%T A309618 6310114560,88168366080,1320468480000,21101183631360,358354687426560,
%U A309618 6444941507297280,122367252835860480,2445878526994022400,51337143210820239360,1128918790687649955840
%N A309618 a(n) = Sum_{k=0..floor(n/2)} k! * 2^k * (n - 2*k)!.
%H A309618 Vaclav Kotesovec, <a href="/A309618/b309618.txt">Table of n, a(n) for n = 0..448</a>
%F A309618 G.f.: B(x)*B(2*x^2), where B(x) is g.f. of A000142.
%F A309618 a(n) ~ n! * (1 + 2/n^2 + 2/n^3 + 10/n^4 + 50/n^5 + 250/n^6 + 1442/n^7 + 9514/n^8 + 68882/n^9 + 539098/n^10 + ...), for coefficients see A326983.
%t A309618 Table[Sum[k!*2^k*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
%t A309618 nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}] * Sum[k!*2^k*x^(2 k), {k, 0, nmax}], {x, 0, nmax}], x]
%Y A309618 Cf. A000142, A003149, A107713, A110143, A309619.
%K A309618 nonn
%O A309618 0,3
%A A309618 _Vaclav Kotesovec_, Aug 10 2019