cp's OEIS Frontend

A184358 a(n) = (n+1)!^2/2^n.

%I A184358 #10 Jun 25 2022 08:25:28
%S A184358 1,2,9,72,900,16200,396900,12700800,514382400,25719120000,
%T A184358 1556006760000,112032486720000,9466745127840000,927741022528320000,
%U A184358 104370865034436000000,13359470724407808000000,1930443519676928256000000,312731850187662377472000000
%N A184358 a(n) = (n+1)!^2/2^n.
%C A184358 Self-convolution of A184359.
%F A184358 From _Amiram Eldar_, Jun 25 2022: (Start)
%F A184358 Sum_{n>=0} 1/a(n) = (BesselI(0, 2*sqrt(2)) - 1)/2.
%F A184358 Sum_{n>=0} (-1)^n/a(n) = (1 - BesselJ(0, 2*sqrt(2)))/2. (End)
%e A184358 G.f.: A(x) = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 +...
%e A184358 A(x)^(1/2) = 1 + x + 4*x^2 + 32*x^3 + 410*x^4 + 7562*x^5 + 188736*x^6 +...+ A184359(n)*x^n +...
%t A184358 a[n_] := (n + 1)!^2/2^n; Array[a, 20, 0] (* _Amiram Eldar_, Jun 25 2022 *)
%o A184358 (PARI) {a(n)=(n+1)!^2/2^n}
%Y A184358 Cf. A184359, A184360, A184361, A006472.
%K A184358 nonn
%O A184358 0,2
%A A184358 _Paul D. Hanna_, Jan 16 2011