A159317 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.

1, 1, 5, 217, 81761, 240072001, 5184101454785, 817326468545940097, 958739380619551186754561, 8575669073854524479684954572801, 596451091280508109580869521043477279745

Offset: 0

Author

Paul D. Hanna, Apr 19 2009

Keywords

• nonn

Comments

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

Examples

			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! +...
The e.g.f. of A159315 is:
F(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 41*x^4/4! + 406*x^5/5! + 7127*x^6/6! +...
		

Crossrefs

Cf. A159314, A159315, A126444.

Programs

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)}

Formula

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(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.