$4n^2\; -\; 3n$

with $n\; >\; 0$. The first few decagonal numbers are

1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326, 8695, 9072, 9457, 9850

The decagonal number for n can also be calculated by adding the square of n to thrice the (n - 1)th pronic number, or to put it algebraically, $D\_n\; =\; n^2\; +\; 3(n^2\; -\; n)$.

Decagonal numbers consistently alternate parity.