A373499 - OEIS

A373499

a(n) = Sum_{i=1..n-1} binomial(prime(n),prime(i)).

0, 3, 20, 77, 1012, 3445, 41208, 166041, 2886776, 176545765, 707922076, 44154219471, 628182427994, 2318296787282, 32073418630027, 2032575090770969, 140272398486718041, 558946109921421607, 34092092791668401412, 554618378100523846567, 2286090868263899514704

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(1) = 0, a(n) = Sum_{i=1..n-1} binomial(A000040(n),A000040(i)).

EXAMPLE

For n = 3, a(3) = binomial(prime(3),prime(1)) + binomial(prime(3),prime(2)) = binomial(5,2) + binomial(5,3) = 10 + 10 = 20.

MATHEMATICA

Table[Sum[Binomial[Prime[n], Prime[i]], {i, n-1}], {n, 25}] (* Paolo Xausa, Jun 29 2024 *)

PROG