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

Offset: 1

Author

Alexandre Herrera, Jun 06 2024

Keywords

• nonn

Examples

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

Crossrefs

Cf. A000040.

Programs

Mathematica

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

PARI

a(n) = sum(i=1, n-1, binomial(prime(n), prime(i))); \\ Michel Marcus, Jun 25 2024

Python

from sympy import binomial
from sympy import prime
def a(n): return sum(binomial(prime(n),prime(i)) for i in range(1,n))
print([a(n) for n in range(1,22)])

Formula

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