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A267096 a(n) = Product_{i=0..n} prime(i+2)^binomial(n,i). 6
3, 15, 525, 1414875, 41985913344375, 433555011900329243987584396875, 3514495551481947615680580256869117013417604971088496013610671875 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 17:32 EST 2021. Contains 349526 sequences. (Running on oeis4.)