A158872 G.f.: A(x) = exp(Sum_{n>=1} A158873(n)*x^n/n) = exp(Sum_{n>=1} (1 + A158873(n)*x)^n*x^n/n).

1, 1, 2, 5, 20, 182, 6552, 1517473, 4654013540, 520378069012098, 10766981089503125653501, 448728931430680787386854758969563, 1010943666488949958707946804366787268947495194377

Offset

0,3

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 182*x^5 + 6552*x^6 +...
Let L(x) = g.f. of A158873 where exp(L(x)) = A(x), then:
L(x) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 796*x^5/5 + 38106*x^6/6 +...
L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+10*x)^3*x^3/3 + (1+59*x)^4*x^4/4 +...

Prog

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

Crossrefs

Cf. A158873 (log).

Sequence in context: A058109 A005331 A261005 * A308522 A216462 A006893

Adjacent sequences: A158869 A158870 A158871 * A158873 A158874 A158875

Keyword

nonn

Author

Paul D. Hanna, Apr 10 2009

Status

approved