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

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

Offset

0,1

Links

Table of n, a(n) for n=0..6.

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

Formula

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

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

Example

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.

Prog

(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)))))))

Crossrefs

Second column (or diagonal from right) in A066117.

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

Sequence in context: A122579 A138303 A338293 * A217449 A167220 A296939

Adjacent sequences: A267093 A267094 A267095 * A267097 A267098 A267099

Keyword

nonn

Author

Antti Karttunen, Feb 06 2016

Status

approved