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a(n) = sum of n-th row of the triangle formed by replacing each m in Pascal's triangle with the m-th prime.
1

%I #6 Mar 31 2017 21:51:57

%S 2,4,7,14,31,84,195,482,1131,2620,5957,13502,29911,65820,143551,

%T 311074,669543,1435388,3061571,6503526,13771989,29061728,61159219,

%U 128372210,268845359,561835492,1171862289,2440014306,5072185867,10528184756

%N a(n) = sum of n-th row of the triangle formed by replacing each m in Pascal's triangle with the m-th prime.

%e The fourth row of Pascal's triangle is 1 3 3 1. Replacing each n by prime(n) gives 2 5 5 2, the terms of which sum to 14. Therefore a(4) = 14.

%t f[n_] := Sum[Prime[Binomial[n-1, i]], {i, 0, n-1}]; Table[f[i], {i, 1, 30}]

%Y Cf. A074589.

%K easy,nonn

%O 1,1

%A _Joseph L. Pe_, Sep 26 2002