A277436 a(n) = |Gamma(n, i)|^2, where i = sqrt(-1).

1, 2, 5, 34, 569, 14426, 518557, 25400810, 1625695409, 131681938834, 13168189962101, 1593350918236562, 229442532743676265, 38775788044161003434, 7600054456561351409549, 1710012252724103327072026, 437763136697393060993682017, 126513546505547193228474910370

Offset: 1

Author

Vladimir Reshetnikov, Oct 14 2016

Keywords

• nonn

Links

• Eric Weisstein's MathWorld, Incomplete Gamma Function

Crossrefs

Cf. A009102, A009551.

Programs

Mathematica

RecurrenceTable[{n (n - 1) (a[n - 1] - (n - 2)^2 a[n - 2] + 1) + a[n + 1] == n^2 a[n] + 1, a[1] == 1, a[2] == 2, a[3] == 5}, a[n], {n, 1, 20}] (* or *)
Round[Abs[Gamma[Range[20], I]]^2]

Formula

a(n) = |Gamma(n, i)|^2 = Gamma(n, i)*Gamma(n, -i), where i = sqrt(-1).

a(n) = A009102(n-1)^2 + A009551(n-1)^2.

Recurrence: n*(n-1)*(a(n-1) - (n-2)^2*a(n-2) + 1) + a(n+1) = n^2*a(n) + 1.

a(n) ~ (n-1)!^2. - Vaclav Kotesovec, Oct 15 2016