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%I #9 Feb 17 2023 18:36:00
%S 1,16,305,4396,43093,332193,87172020,273879343
%N a(n) is the smallest positive integer which can be represented as the sum of n distinct binomial coefficients binomial(k,n) for some k >= n in exactly n ways, or -1 if no such integer exists.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialCoefficient.html">Binomial Coefficient</a>
%e For n = 2: 16 = C(2,2) + C(6,2) = C(4,2) + C(5,2) = 1 + 15 = 6 + 10.
%e For n = 3: 305 = C(3,3) + C(9,3) + C(12,3) = C(6,3) + C(10,3) + C(11,3) = C(8,3) + C(9,3) + C(11,3) = 1 + 84 + 220 = 20 + 120 + 165 = 56 + 84 + 165.
%e For n = 4: 4396 = C(5,4) + C(11,4) + C(14,4) + C(18,4) = C(8,4) + C(9,4) + C(16,4) + C(17,4) = C(9,4) + C(12,4) + C(13,4) + C(18,4) = C(10,4) + C(14,4) + C(15,4) + C(16,4) = 5 + 330 + 1001 + 3060 = 70 + 126 + 1820 + 2380 = 126 + 495 + 715 + 3060 = 210 + 1001 + 1365 + 1820.
%Y Cf. A007318, A350288, A360217.
%K nonn,more
%O 1,2
%A _Ilya Gutkovskiy_, Feb 07 2023
%E a(8) from _Michael S. Branicky_, Feb 17 2023