

A267096


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


6




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



