A267096 a(n) = Product_{i=0..n} prime(i+2)^binomial(n,i).

3, 15, 525, 1414875, 41985913344375, 433555011900329243987584396875, 3514495551481947615680580256869117013417604971088496013610671875

Offset: 0

Author

Antti Karttunen, Feb 06 2016

Keywords

• nonn

Examples

			Terms are obtained by exponentiating the odd primes in range [3 .. prime(2+n)] with the binomial coefficients obtained from row n of Pascal's triangle (A007318) and then multiplying the factors together:
            3^1
         3^1 * 5^1
      3^1 * 5^2 * 7^1
   3^1 * 5^3 * 7^3 * 11^1
3^1 * 5^4 * 7^6 * 11^4 * 13^1
etc.
		

Links

• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Second column (or diagonal from right) in A066117.

Cf. A000040, A003961, A007188, A007318, A252738, A276804.

Programs

Scheme

(define (A267096 n) (mul (lambda (k) (expt (A000040 (+ 2 k)) (A007318tr n k))) 0 n)) ;; Where A007318tr gives binomial coefficients, as in A007318.
(define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (1+ i) (* res (intfun i)))))))

Formula

a(n) = Product_{i=0..n} prime(i+2)^C(n,i).

a(n) = A003961(A007188(n)).