A159317 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,1,5,217,81761,240072001,5184101454785,817326468545940097,

%T 958739380619551186754561,8575669073854524479684954572801,

%U 596451091280508109580869521043477279745

%N a(n)/2^(n^2) is the coefficient of x^n/n! in F(x)^(1/2^n) where F(x) is the e.g.f. of A159315.

%C Equals main diagonal of array A159314; A159315 equals row 0 of array A159314.

%F E.g.f.: Sum_{n>=0} a(n)/2^(n^2)*x^n/n! = Sum_{n>=0} log(F(x/2^n))^n/n! where F(x) is the e.g.f. of A159315.

%F F(x)^(1/2^n) = R(n,x/2^n) where F(x)=R(0,x) and R(n,x) is the e.g.f. of row n of array A159314.

%e E.g.f.: 1 + 1/2*x + 5/2^4*x^2/2! + 217/2^9*x^3/3! + 81761/2^16*x^4/4! +...

%e The e.g.f. of A159315 is:

%e F(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 41*x^4/4! + 406*x^5/5! + 7127*x^6/6! +...

%o (PARI) {a(n)=local(A=vector(2*n+2, j, 1+j*x)); for(i=0, 2*n+1, for(j=0, 2*n, m=2*n+1-j; A[m]=exp(intformal((A[m+1]+x*O(x^n))^(2^(m-1)))))); n!*polcoeff(A[n+1], n, x)}

%Y Cf. A159314, A159315, A126444.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 19 2009