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%I #10 Aug 23 2022 12:12:49
%S 1,2,5,10,26,58,167,414,1324,3606,12729,37674,145578,463770,1944879,
%T 6614190,29852856,107616150,518782545,1970493210,10077228270,
%U 40125873690,216425656215,899557170750,5091758227620,22011865939350,130202223160905,583641857191050,3594820517111250
%N a(n) = Sum_{k=0..n} k!!*(n - k)!!.
%C Convolution of A006882 with itself.
%H Alois P. Heinz, <a href="/A305577/b305577.txt">Table of n, a(n) for n = 0..807</a>
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F G.f.: (Sum_{k>=0} k!!*x^k)^2.
%p a:= proc(n) option remember; `if`(n<4, n^2+1,
%p ((3*n^2-4*n-2)*a(n-2) +(n+1)*a(n-3)
%p -2*a(n-1) -(n-1)^2*n*a(n-4))/(2*n-4))
%p end:
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jun 14 2018
%t Table[Sum[k!! (n - k)!!, {k, 0, n}], {n, 0, 28}]
%t nmax = 28; CoefficientList[Series[Sum[k!! x^k, {k, 0, nmax}]^2, {x, 0, nmax}], x]
%Y Cf. A003149, A006882, A034430, A059371, A111308, A126674, A305578.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jun 05 2018