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a(n) = Sum((1+p_1)*(1+p_2)*...)*(1+p_m)), summation being over all compositions (p_1, p_2, ..., p_m) of n. Example: a(3)=24; indeed, the compositions of 3 are (1,1,1), (1,2), (2,1), (3) and we have 2*2*2 + 2*3 + 3*2 + 4 = 24. - Emeric Deutsch, Oct 17 2010
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1, 2, 7, 24, 82, 280, 956, 3264, 11144, 38048, 129904, 443520, 1514272, 5170048, 17651648, 60266496, 205762688, 702517760, 2398545664, 8189147136, 27959497216, 95459694592, 325919783936, 1112759746560, 3799199418368, 12971278180352, 44286713884672, 151204299177984
D. Battaglino, J. M. Fedou, S. Rinaldi , and S. Socci, <a href="https://doi.org/10.46298/dmtcs.2370">The number of k-parallelogram polyominoes</a>, FPSAC 2013 Paris, France DMTCS Proc. AS, 2013, 1143-1154.
G. Castiglione, A. Frosini, E. Munarini, A. Restivo , and S. Rinaldi, <a href="http://dx.doi.org/10.1016/j.ejc.2006.06.020">Combinatorial aspects of L-convex polyominoes</a>, European J. Combin. 28 (2007), no. 6, 1724-1741.
E. Duchi, S. Rinaldi , and G. Schaeffer, <a href="https://arxiv.org/abs/math/0602124">The number of Z-convex polyominoes</a>, arXiv:math/0602124 [math.CO], 2006.