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%I #16 Mar 02 2023 02:58:07
%S 1,18,1200,176400,45722880,18441561600,10685567692800,
%T 8414884558080000,8646761377013760000,11237331085567082496000,
%U 18020592759036666839040000,34953943088278121445457920000,80662945588334126412595200000000,218412210097326433146332774400000000
%N a(n) = ((2*n + 1)! / n!)^2 / (n + 1).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModifiedStruveFunction.html">Modified Struve Function</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StruveFunction.html">Struve function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Struve_function">Struve function</a>.
%F a(n) = CatalanNumber(n) * (2*n)! * (2*n + 1)^2.
%F a(n) ~ (4*n/e)^(2*n)*(8*n - 2/3).
%F From _Amiram Eldar_, Mar 02 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 1/2 + StruveL(0, 1/2)*Pi/2 + StruveL(1, 1/2)*Pi/4, where StruveL is the modified Struve function.
%F Sum_{n>=0} (-1)^n/a(n) = 1/2 + StruveH(0, 1/2)*Pi/2 - StruveH(1, 1/2)*Pi/4, where StruveH is the Struve function. (End)
%p a := n -> ((2*n + 1)! / n!)^2 / (n + 1):
%p seq(a(n), n = 0..13);
%t a[n_] := ((2*n + 1)!/n!)^2/(n + 1); Array[a, 14, 0] (* _Amiram Eldar_, Mar 02 2023 *)
%Y Cf. A122747, A000108, A000407.
%K nonn
%O 0,2
%A _Peter Luschny_, Feb 16 2023
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