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%I #26 Sep 22 2021 07:43:26
%S 1,0,1,0,2,1,0,1,4,1,0,1,7,9,1,0,0,4,28,15,1,0,0,2,47,91,26,1,0,0,0,
%T 27,268,257,40,1,0,0,0,10,312,1318,643,62,1,0,0,0,1,137,2807,5347,
%U 1511,91,1,0,0,0,1,35,2204,19516,19453,3331
%N Triangle T(n, d) = the number of isomorphism classes of smooth Fano d-polytopes with n vertices, read by rows (n >= 2, 1 <= d < n).
%H Mikkel Obro, <a href="https://arXiv.org/abs/0704.0049">An algorithm for the classification of smooth Fano polytopes</a>, arXiv:0704.0049 [math.CO], Apr 02 2007, p. 15.
%H Mikkel Øbro, <a href="https://pure.au.dk/ws/files/41742384/imf_phd_2008_moe.pdf">Classification of smooth Fano polytopes</a>, PhD thesis, 2007. See Appendix A.
%H Andreas Paffenholz, <a href="https://polymake.org/polytopes/paffenholz/www/fano.html">Smooth Reflexive Lattice Polytopes</a>
%e Table begins:
%e n |d=1|d=2|d=3|d=4|d=5|d=6|d=7
%e 1 |
%e 2 | 1 |
%e 3 | | 1 |
%e 4 | | 2 | 1 |
%e 5 | | 1 | 4 | 1 |
%e 6 | | 1 | 7 | 9 | 1 |
%e 7 | | | 4 | 28| 15| 1 |
%e 8 | | | 2 | 47| 91| 26| 1
%e 9 | | | | 27|268|257| 40
%Y Column sums are A140296.
%K nonn,tabl
%O 2,5
%A _Jonathan Vos Post_, Apr 03 2007
%E Edited and leading zeroes in rows and few more values added by _Andrey Zabolotskiy_, Sep 19 2018
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