%I #8 Dec 23 2014 00:38:44
%S 1,2,6,360,102060000,70740876785040000000000,
%T 4202178315558341781781575963435449520000000000000000000000000
%N a(n) = A252738(n) / n!
%F a(n) = A252738(n) / A000142(n).
%o (PARI)
%o allocatemem(234567890);
%o 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 A252741print(up_to_n) = { my(s, i=0, n=0); for(n=0, up_to_n, if(0 == n, s = 1, if(1 == n, s = 2; lev = vector(1); lev[1] = 2, oldlev = lev; lev = vector(2*length(oldlev)); s = 1; for(i = 0, (2^(n-1))-1, lev[i+1] = if((i%2),A003961(oldlev[(i\2)+1]),2*oldlev[(i\2)+1]); s *= lev[i+1]))); write("b252741.txt", n, " ", s/n!)); };
%o A252741print(6); \\ Produces the same terms.
%o (Scheme) (define (A252741 n) (/ (A252738 n) (A000142 n)))
%Y Cf. A000142, A252738, A252739, A252740.
%Y See also comments at A005940 and A163511.
%K nonn
%O 0,2
%A _Antti Karttunen_, Dec 21 2014