Indices under consideration, n

Binomial coefficients

0

1

1

1, 1

3

1, 3, 3, 1

7

1, 7, 21, 35, 35, 21, 7, 1

15

1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1

31

1, 31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315, 44352165, 20160075, 7888725, 2629575, 736281, 169911, 31465, 4495, 465, 31, 1

63

1, 63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475, 13488561475572645, 27619435402363035, 52728013040874885, 93993414551124795, 156655690918541325, 244382877832924467, 357174975294274221, 489462003181042451, 629308289804197437, 759510004936100355, 860778005594247069, 916312070471295267, 860778005594247069, 759510004936100355, 629308289804197437, 489462003181042451, 357174975294274221, 244382877832924467, 156655690918541325, 93993414551124795, 52728013040874885, 27619435402363035, 13488561475572645, 6131164307078475, 2588713818544245, 1012974972473835, 366395202809685, 122131734269895, 37387265592825, 10468434365991, 2668424446233, 615790256823, 127805525001, 23667689815, 3872894697, 553270671, 67945521, 7028847, 595665, 39711, 1953, 63, 1