cp's OEIS Frontend

A199875 G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n*A(x)^n/n ).

%I A199875 #8 Mar 30 2012 18:37:32
%S A199875 1,1,3,12,51,233,1126,5639,29001,152364,814268,4412733,24193883,
%T A199875 133964582,748084930,4208233719,23825366565,135657095301,776310257573,
%U A199875 4462597387720,25757503356976,149216036734018,867316809868018,5056666312351966,29564095191382323
%N A199875 G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n*A(x)^n/n ).
%F A199875 G.f. satisfies: A(x) = G(x*A(x)) where G(x) = A(x/G(x)) is the g.f. of A198950.
%e A199875 G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 51*x^4 + 233*x^5 + 1126*x^6 +...
%e A199875 where
%e A199875 log(A(x)) = (1 + x)*x*A(x) + (1 + 2^3*x + x^2)*x^2*A(x)^2/2 +
%e A199875 (1 + 3^3*x + 3^3*x^2 + x^3)*x^3*A(x)^3/3 +
%e A199875 (1 + 4^3*x + 6^3*x^2 + 4^3*x^3 + x^4)*x^4*A(x)^4/4 +
%e A199875 (1 + 5^3*x + 10^3*x^2 + 10^3*x^3 + 5^3*x^4 + x^5)*x^5*A(x)^5/5 +...
%e A199875 more explicitly,
%e A199875 log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 149*x^4/4 + 821*x^5/5 + 4664*x^6/6 + 26839*x^7/7 +...
%e A199875 The g.f. satisfies A(x) = G(x*A(x)) where G(x) is the g.f. of A198950:
%e A199875 G(x) = 1 + x + 2*x^2 + 5*x^3 + 10*x^4 + 22*x^5 + 58*x^6 + 150*x^7 + 392*x^8 +...
%o A199875 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3*x^j)*(x*A+x*O(x^n))^m/m))); polcoeff(A, n, x)}
%Y A199875 Cf. A198950.
%K A199875 nonn
%O A199875 0,3
%A A199875 _Paul D. Hanna_, Nov 11 2011