A343414 - OEIS

%I #9 Apr 14 2021 22:27:22

%S 2,8,31,105,353,1039,2961,7859,20437,53015,131605,325097,787137,

%T 1857829,4334237,10072829,23286445,52990531,120131489,270138397,

%U 601071655,1334201393,2945054825,6485229057,14277775651,31269827137,68032540043,147446383463,317906538223,683411440339,1475890477529

%N a(n) = Sum_{i=1..n+1} prime(i)*Sum_{j=0..i-1} binomial(n,j).

%H Robert Israel, <a href="/A343414/b343414.txt">Table of n, a(n) for n = 0..3293</a>

%e a(3) = 2*1+3*(1+3)+5*(1+3+3)+7*(1+3+3+1) = 105.

%p f:= proc(n) local L,i;

%p    L:= ListTools:-PartialSums([seq(binomial(n,i),i=0..n)]);

%p    add(L[i]*ithprime(i),i=1..n+1);

%p end proc:

%p map(f, [$0..40]);

%Y Cf. A343415.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 14 2021