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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 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.)