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A158109 G.f.: A(x) = exp(Sum_{n>=1} C(2n-1,n)*L(n)*x^n/n) such that Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)) where L(n) = A158259(n) and C(2n-1,n) = A001700(n-1). 1

%I #2 Mar 30 2012 18:37:16

%S 1,1,2,15,479,58981,27087299,46407723445,298505825690021,

%T 7255847001783419768,670260315103084510835973,

%U 236409648316126537191063108559,319643614642063671478190549232176669

%N G.f.: A(x) = exp(Sum_{n>=1} C(2n-1,n)*L(n)*x^n/n) such that Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)) where L(n) = A158259(n) and C(2n-1,n) = A001700(n-1).

%e G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 479*x^4 + 58981*x^5 +...

%e log(1+x*A(x)) = x + 1*x^2/2 + 4*x^3/3 + 53*x^4/4 + 2321*x^5/5 +...

%e log(A(x)) = x + 3*x^2/2 + 40*x^3/3 + 1855*x^4/4 + 292446*x^5/5 +...

%e log(A(x)) = x + 3*1*x^2/2 + 10*4*x^3/3 + 35*53*x^4/4 + 126*2321*x^5/5 +...

%o (PARI) {a(n)=local(A=1+x);if(n==0,1,for(i=1,n,A=exp(sum(m=1,n,binomial(2*m-1,m)*x^m*polcoeff(log(1+x*A+x*O(x^m)),m))+x*O(x^n)));polcoeff(A,n))}

%Y Cf. A158259, A158257 (variant), A001700.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 28 2009

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Last modified March 5 08:03 EST 2024. Contains 370538 sequences. (Running on oeis4.)