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 A309619 #13 Dec 08 2020 02:26:25
%S A309619 1,1,3,7,28,128,754,5178,41124,368220,3670872,40290744,482716896,
%T A309619 6267697920,87664818960,1313983544400,21010949076960,357007805477280,
%U A309619 6423473819220480,122003441554176000,2439346762501367040,51213306647556506880,1126446562222595147520
%N A309619 a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.
%H A309619 Vaclav Kotesovec, <a href="/A309619/b309619.txt">Table of n, a(n) for n = 0..448</a>
%F A309619 G.f.: B(x)*B(x^2), where B(x) is g.f. of A000142.
%F A309619 a(n) ~ n! * (1 + 1/n^2 + 1/n^3 + 3/n^4 + 13/n^5 + 57/n^6 + 271/n^7 + 1467/n^8 + 8905/n^9 + 58965/n^10 + ...), for coefficients see A326984.
%t A309619 nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}]*Sum[k!*x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
%t A309619 Table[Sum[k!*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
%o A309619 (PARI) a(n) = sum(k=0, n\2, k! * (n - 2*k)!); \\ _Michel Marcus_, Dec 08 2020
%Y A309619 Cf. A000142, A003149, A096161, A107713, A309618, A339515.
%K A309619 nonn
%O A309619 0,3
%A A309619 _Vaclav Kotesovec_, Aug 10 2019