A090347 Number of labeled trees with n nodes and even number of leaves minus number of labeled trees with n nodes and odd number of leaves.

1, 3, 8, 5, -156, -1253, 48, 116937, 1236140, -4517689, -317599800, -3473788019, 43408737540, 2033846838675, 19004486417504, -643679274285679, -24665731809676452, -135665006897593601, 15018201730467027960

Offset: 2

Author

Vladeta Jovovic, Jan 28 2004

Keywords

• sign

Crossrefs

Cf. A055314.

Formula

Sum_{k=0..n} (-1)^k*n!/k!*stirling2(n-2, n-k).