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, 1, 2, 15, 479, 58981, 27087299, 46407723445, 298505825690021, 7255847001783419768, 670260315103084510835973, 236409648316126537191063108559, 319643614642063671478190549232176669

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 479*x^4 + 58981*x^5 +...
log(1+x*A(x)) = x + 1*x^2/2 + 4*x^3/3 + 53*x^4/4 + 2321*x^5/5 +...
log(A(x)) = x + 3*x^2/2 + 40*x^3/3 + 1855*x^4/4 + 292446*x^5/5 +...
log(A(x)) = x + 3*1*x^2/2 + 10*4*x^3/3 + 35*53*x^4/4 + 126*2321*x^5/5 +...

Prog

(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))}

Crossrefs

Cf. A158259, A158257 (variant), A001700.

Sequence in context: A013059 A013098 A365534 * A370014 A357856 A177394

Adjacent sequences: A158106 A158107 A158108 * A158110 A158111 A158112

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2009

Status

approved