A265750 Prime factorization representation of polynomials defined recursively by p(0,x)=1 and for n>0: p(n,x) = x*p(n-1,x) + 4n+2. (See A192750).

2, 192, 3732480, 105815808000000, 15845956399848960000000000, 64521196676588557133336908800000000000000, 11596208520592232147315615803672416545196288000000000000000000, 254410805372253907145905144265082090216385314644252349615132618240000000000000000000000

Offset: 0

Author

Antti Karttunen, Dec 15 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A003961, A192750, A192751, A206296, A265752, A265753.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A265750(n) = if(0==n, 2, A003961(A265750(n-1)) * 2^((4*n)+2));
for(n=0, 10, write("b265750.txt", n, " ", A265750(n)));

Scheme

(definec (A265750 n) (if (zero? n) 2 (* (A003961 (A265750 (- n 1))) (A000079 (+ 2 (* 4 n))))))

Formula

a(0) = 2; for n >= 1, a(n) = A003961(a(n-1)) * 2^((4*n)+2).

Other identities. For all n >= 1:

A192750(n) = A265752(a(n)).

A192751(n) = A265753(a(n)).