A179501 - OEIS

%I #2 Mar 30 2012 18:37:22

%S 1,3,10,43,276,3138,80998,7043187,3719589796,27895892650378,

%T 9982024484486217164,953757232905143490078932902,

%U 293418537539006210065580840496997061594

%N Logarithmic derivative of A179500.

%C The g.f. of A179500, G(x), is defined by:

%C . G(x) = exp( Sum_{n>=1} [Sum_{k>=0} A179500(k)^n* x^k]^n* x^n/n );

%C the g.f. of this sequence is L(x) = log(G(x)).

%e L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 276*x^5/5 +...

%e The g.f. of A179500, G(x) = exp(L(x)), begins:

%e G(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 + 612*x^6 + 12271*x^7+...

%e where L(x) = log(G(x)) equals the series:

%e L(x) = (1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 +...)*x

%e + (1 + x + 2^2*x^2 + 5^2*x^3 + 16^2*x^4 + 74^2*x^5 +...)^2*x^2/2

%e + (1 + x + 2^3*x^2 + 5^3*x^3 + 16^3*x^4 + 74^3*x^5 +...)^3*x^3/3

%e + (1 + x + 2^4*x^2 + 5^4*x^3 + 16^4*x^4 + 74^4*x^5 +...)^4*x^4/4

%e + (1 + x + 2^5*x^2 + 5^5*x^3 + 16^5*x^4 + 74^5*x^5 +...)^5*x^5/5 +...

%o (PARI) {a(n)=local(L,G,A179500);G=exp(x+sum(k=2,n-1,a(k)*x^k/k)+x*O(x^n));A179500=Vec(G); L=sum(m=1,n,sum(k=0,n-m,A179500[k+1]^m*x^k+x*O(x^n))^m*x^m/m);n*polcoeff(L,n)}

%Y Cf. A179501.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 21 2010