# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a343414 Showing 1-1 of 1 %I A343414 #9 Apr 14 2021 22:27:22 %S A343414 2,8,31,105,353,1039,2961,7859,20437,53015,131605,325097,787137, %T A343414 1857829,4334237,10072829,23286445,52990531,120131489,270138397, %U A343414 601071655,1334201393,2945054825,6485229057,14277775651,31269827137,68032540043,147446383463,317906538223,683411440339,1475890477529 %N A343414 a(n) = Sum_{i=1..n+1} prime(i)*Sum_{j=0..i-1} binomial(n,j). %H A343414 Robert Israel, Table of n, a(n) for n = 0..3293 %e A343414 a(3) = 2*1+3*(1+3)+5*(1+3+3)+7*(1+3+3+1) = 105. %p A343414 f:= proc(n) local L,i; %p A343414 L:= ListTools:-PartialSums([seq(binomial(n,i),i=0..n)]); %p A343414 add(L[i]*ithprime(i),i=1..n+1); %p A343414 end proc: %p A343414 map(f, [$0..40]); %Y A343414 Cf. A343415. %K A343414 nonn %O A343414 0,1 %A A343414 _J. M. Bergot_ and _Robert Israel_, Apr 14 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE