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a(n) = exp(2) * Sum_{i>=0} Sum_{j>=0} (-1)^(i+j) * (i*j)^n / (i! * j!).
0

%I #5 Aug 13 2020 08:58:45

%S 1,1,0,1,1,4,81,81,2500,71289,170569,4752400,314388361,2553584089,

%T 12138750976,3868290439209,98777141491561,74627448683524,

%U 77548359598953721,6456459980629467081,96370747288471888164,738333256838429983201,526354651474052521626801

%N a(n) = exp(2) * Sum_{i>=0} Sum_{j>=0} (-1)^(i+j) * (i*j)^n / (i! * j!).

%C Squares of complementary Bell numbers.

%F a(n) = A000587(n)^2.

%t Table[Exp[2] Sum[Sum[(-1)^(i + j) (i j)^n/(i! j!), {j, 0, Infinity}], {i, 0, Infinity}], {n, 0, 22}]

%t Table[BellB[n, -1]^2, {n, 0, 22}]

%Y Cf. A000587, A001247, A121869.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Aug 12 2020