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A343414
a(n) = Sum_{i=1..n+1} prime(i)*Sum_{j=0..i-1} binomial(n,j).
2
2, 8, 31, 105, 353, 1039, 2961, 7859, 20437, 53015, 131605, 325097, 787137, 1857829, 4334237, 10072829, 23286445, 52990531, 120131489, 270138397, 601071655, 1334201393, 2945054825, 6485229057, 14277775651, 31269827137, 68032540043, 147446383463, 317906538223, 683411440339, 1475890477529
OFFSET
0,1
LINKS
EXAMPLE
a(3) = 2*1+3*(1+3)+5*(1+3+3)+7*(1+3+3+1) = 105.
MAPLE
f:= proc(n) local L, i;
L:= ListTools:-PartialSums([seq(binomial(n, i), i=0..n)]);
add(L[i]*ithprime(i), i=1..n+1);
end proc:
map(f, [$0..40]);
CROSSREFS
Cf. A343415.
Sequence in context: A007468 A280156 A054137 * A062456 A289610 A077838
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Apr 14 2021
STATUS
approved