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A307349 a(n) = Sum_{i=1..n} Sum_{j=1..n} (-1)^(i+j) * (i+j)!/(2!*i!*j!).

%I A307349 #24 Jul 11 2019 11:14:29
%S A307349 0,1,1,5,15,56,203,757,2839,10736,40821,155948,598065,2301118,8878591,
%T A307349 34340085,133100055,516851528,2010358061,7831136920,30546063745,
%U A307349 119291436738,466379022561,1825168170620,7149316835465,28027993191706,109965636641173
%N A307349 a(n) = Sum_{i=1..n} Sum_{j=1..n} (-1)^(i+j) * (i+j)!/(2!*i!*j!).
%H A307349 Seiichi Manyama, <a href="/A307349/b307349.txt">Table of n, a(n) for n = 0..1665</a>
%F A307349 a(n) = (A120305(n) - (-1)^n)/2. - _Vaclav Kotesovec_, Apr 03 2019
%F A307349 a(n) ~ 2^(2*n+1) / (9*sqrt(Pi*n)). - _Vaclav Kotesovec_, Apr 03 2019
%F A307349 G.f.: (1/sqrt(1-4*z)-1+2*z/(1-z^2))/(2*(2+z)). - _Sergey Perepechko_, Jul 11 2019
%t A307349 Table[Sum[Sum[(-1)^(i + j)*(i + j)!/(2*i!*j!), {i, 1, n}], {j, 1, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Apr 03 2019 *)
%o A307349 (PARI) {a(n) = sum(i=1, n, sum(j=1, n, (-1)^(i+j)*(i+j)!/(2*i!*j!)))}
%o A307349 (PARI) {a(n) = sum(i=2, 2*n, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^2, i))/2} \\ _Seiichi Manyama_, May 20 2019
%Y A307349 Cf. A048775, A120305, A307350, A307351.
%K A307349 nonn
%O A307349 0,4
%A A307349 _Seiichi Manyama_, Apr 03 2019