A158259 L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*exp(Sum_{n>=1} C(2n-1,n)*a(n)*x^n/n) where C(2n-1,n) = A001700(n-1).

1, 1, 4, 53, 2321, 351010, 189198136, 371045084781, 2686134761118382, 72555484959298332681, 7372783651816395650943931, 2836907736669733620359204710274, 4155363917021399525198623243750199333

Offset

0,3

Links

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

Formula

L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*G(x) where G(x) = g.f. of A158109.

exp(Sum_{n>=1} a(n)*x^n/n) = [1 + Sum_{n>=1} C(2n-1,n)*a(n)*x^n]/[1 + Sum_{n>=1} (C(2n-1,n)-1)*a(n)*x^n].

Example

L.g.f.: A(x) = x + 1*x^2/2 + 4*x^3/3 + 53*x^4/4 + 2321*x^5/5 +...
exp(A(x)) = 1 + x + 2*x^2 + 15*x^3 + 479*x^4 + 58981*x^5 +...
exp(A(x)) = 1 + x*G(x) where G(x) is the g.f. of A158109 such that:
log(G(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=x+x^2); if(n==0, 1, for(i=1, n-1, A=log(1+x*exp(sum(m=1, n, binomial(2*m-1, m)*x^m*polcoeff(A+x*O(x^m), m) )+x*O(x^n)))); n*polcoeff(A, n))}

Crossrefs

Cf. A158109, A158258 (variant), A001700.

Sequence in context: A221605 A307172 A275801 * A362050 A095210 A156469

Adjacent sequences: A158256 A158257 A158258 * A158260 A158261 A158262

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2009

Status

approved