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 A305577 #11 Feb 16 2025 08:33:54
%S A305577 1,2,5,10,26,58,167,414,1324,3606,12729,37674,145578,463770,1944879,
%T A305577 6614190,29852856,107616150,518782545,1970493210,10077228270,
%U A305577 40125873690,216425656215,899557170750,5091758227620,22011865939350,130202223160905,583641857191050,3594820517111250
%N A305577 a(n) = Sum_{k=0..n} k!!*(n - k)!!.
%C A305577 Convolution of A006882 with itself.
%H A305577 Alois P. Heinz, <a href="/A305577/b305577.txt">Table of n, a(n) for n = 0..807</a>
%H A305577 Poloni, Federico; Del Corso, Gianna M. <a href="https://doi.org/10.1016/j.laa.2017.06.042">Counting Fiedler pencils with repetitions</a>. Linear Algebra Appl. 532, 463-499 (2017), corollary 24.
%H A305577 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>
%H A305577 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A305577 G.f.: (Sum_{k>=0} k!!*x^k)^2.
%p A305577 a:= proc(n) option remember; `if`(n<4, n^2+1,
%p A305577 ((3*n^2-4*n-2)*a(n-2) +(n+1)*a(n-3)
%p A305577 -2*a(n-1) -(n-1)^2*n*a(n-4))/(2*n-4))
%p A305577 end:
%p A305577 seq(a(n), n=0..35); # _Alois P. Heinz_, Jun 14 2018
%t A305577 Table[Sum[k!! (n - k)!!, {k, 0, n}], {n, 0, 28}]
%t A305577 nmax = 28; CoefficientList[Series[Sum[k!! x^k, {k, 0, nmax}]^2, {x, 0, nmax}], x]
%Y A305577 Cf. A003149, A006882, A034430, A059371, A111308, A126674, A305578.
%K A305577 nonn
%O A305577 0,2
%A A305577 _Ilya Gutkovskiy_, Jun 05 2018