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Table[n Sum[Binomial[n, j], {j, n}], {n, 0, 30}] (* or *)
(PARI) { for (n=0, 250, write("b066524.txt", n, " ", n*(2^n - 1)) ) } \\ Harry J. Smith, Feb 21 2010
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Form a triangle in which interior members T(i,j) = T(i-1,j-1) + T(i-1,j). The exterior members are given by 1,2,3,...,2*n-1: T(1,1) = n, T(2,1) = n-1, T(3,1) = n-2, ..., T(n,1) = 1 and T(2,2) = n + 1, T(3,3) = n + 2, ..., T(n,n) = 2*n - 1. The sum of all members will reproduce this sequence. For example, with n = 4 the exterior members are 1 to 7: row(1) = 4; row(2) = 3,5; row(3) = 2,8,6; row(4) = 1,10,14,7. The sum of all these members is 60, the fourth term in the sequence. - J. M. Bergot, Oct 16 2012
a(n) = n * sum_Sum_{j = 1..n} Cbinomial(n,j), n >= 0. - Zerinvary Lajos, May 10 2007
(MAGMAMagma) [n*(2^n-1): n in [0..30]]; // Vincenzo Librandi, Jan 24 2016
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