A157312 - OEIS

%I #3 Mar 30 2012 18:37:16

%S 1,1,1,2,5,18,84,481,3249,25359,224000,2208441,24019991,285633470,

%T 3685413373,51271476627,764944009086,12182390286127,206262410584138,

%U 3699483818281188,70067511789111404,1397379232420943285

%N G.f.: A(x) = exp(Sum_{n>=1} A157311(n)*x^n/n) = Product_{n>=1} (1 + A157311(n-1)*x^n).

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 18*x^5 + 84*x^6 +...

%e where both the exponential:

%e A(x) = exp(x + x^2/2 + 4*x^3/3 + 13*x^4/4 + 66*x^5/5 + 394*x^6/6 +...)

%e and the product:

%e A(x) = (1 + x)(1 + x^2)(1 + x^3)(1 + 4*x^4)(1 + 13*x^5)(1 + 66*x^6)*...

%e generate A(x) using the same coefficients (after initial term):

%e A157311=[1,1,1,4,13,66,394,2759,22005,198049,1979646,21776107,...].

%Y Cf. A157311.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Mar 10 2009