A337053 a(n) = exp(2) * Sum_{i>=0} Sum_{j>=0} (-1)^(i+j) * (i*j)^n / (i! * j!).

1, 1, 0, 1, 1, 4, 81, 81, 2500, 71289, 170569, 4752400, 314388361, 2553584089, 12138750976, 3868290439209, 98777141491561, 74627448683524, 77548359598953721, 6456459980629467081, 96370747288471888164, 738333256838429983201, 526354651474052521626801

Offset: 0

Author

Ilya Gutkovskiy, Aug 12 2020

Keywords

• nonn

Comments

Squares of complementary Bell numbers.

Crossrefs

Cf. A000587, A001247, A121869.

Programs

Mathematica

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

Formula

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