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 A305578 #8 Feb 16 2025 08:33:54
%S A305578 1,2,6,18,64,230,936,3822,17344,78354,389280,1913010,10267776,
%T A305578 54235350,311348352,1751907150,10673326080,63531238050,408231498240,
%U A305578 2556121021650,17236028160000,113006008398150,796296326031360,5445783239554350,39959419088977920,284127133728611250
%N A305578 a(n) = Sum_{k=0..n} binomial(n,k)*k!!*(n - k)!!.
%C A305578 Exponential convolution of A006882 with itself.
%H A305578 Alois P. Heinz, <a href="/A305578/b305578.txt">Table of n, a(n) for n = 0..730</a>
%H A305578 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>
%H A305578 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A305578 E.g.f.: (1 + x*exp(x^2/2)*(1 + sqrt(Pi/2)*erf(x/sqrt(2))))^2.
%p A305578 a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 18][n+1],
%p A305578 3*n*a(n-2)-2*(n-3)*n*a(n-4))
%p A305578 end:
%p A305578 seq(a(n), n=0..30); # _Alois P. Heinz_, Jun 14 2018
%t A305578 Table[Sum[Binomial[n, k] k!! (n - k)!!, {k, 0, n}], {n, 0, 25}]
%t A305578 nmax = 25; CoefficientList[Series[(1 + x Exp[x^2/2] (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]]))^2, {x, 0, nmax}], x] Range[0, nmax]!
%Y A305578 Cf. A000165, A001563, A002866, A006882, A305577.
%K A305578 nonn
%O A305578 0,2
%A A305578 _Ilya Gutkovskiy_, Jun 05 2018