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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).

%I A265750 #9 Dec 18 2015 11:34:30
%S A265750 2,192,3732480,105815808000000,15845956399848960000000000,
%T A265750 64521196676588557133336908800000000000000,
%U A265750 11596208520592232147315615803672416545196288000000000000000000,254410805372253907145905144265082090216385314644252349615132618240000000000000000000000
%N 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).
%H A265750 Antti Karttunen, <a href="/A265750/b265750.txt">Table of n, a(n) for n = 0..10</a>
%F A265750 a(0) = 2; for n >= 1, a(n) = A003961(a(n-1)) * 2^((4*n)+2).
%F A265750 Other identities. For all n >= 1:
%F A265750 A192750(n) = A265752(a(n)).
%F A265750 A192751(n) = A265753(a(n)).
%o A265750 (PARI)
%o A265750 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
%o A265750 A265750(n) = if(0==n, 2, A003961(A265750(n-1)) * 2^((4*n)+2));
%o A265750 for(n=0, 10, write("b265750.txt", n, " ", A265750(n)));
%o A265750 (Scheme) (definec (A265750 n) (if (zero? n) 2 (* (A003961 (A265750 (- n 1))) (A000079 (+ 2 (* 4 n))))))
%Y A265750 Cf. A003961, A192750, A192751, A206296, A265752, A265753.
%K A265750 nonn
%O A265750 0,1
%A A265750 _Antti Karttunen_, Dec 15 2015