A202519 G.f. satisfies: A(x) = exp( Sum_{n>=1} (2*A(x) + (-1)^n)^n * x^n/n ).

1, 1, 7, 27, 165, 877, 5451, 32887, 210505, 1347865, 8859695, 58647219, 393704205, 2662542565, 18166847507, 124738843247, 861922384657, 5986483380145, 41780493605719, 292817777533259, 2060138522838645, 14544377538584925, 103007560370361691, 731635362026777831

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f. satisfies: A(x) = 1/(1-2*x*A(x)) * exp( Sum_{n>=1} (-1)^n/(1 - (-1)^n*2*x*A(x))^n * x^n/n ).

G.f. satisfies: A(x) = sqrt( (1 - (2*A(x)-1)^2*x^2)/(1 - (2*A(x)+1)^2*x^2) ) / (1 - (2*A(x)-1)*x).

G.f. satisfies: 0 = -(1-x) - 2*x*A(x) + (1-x)*(1+x)^2*A(x)^2 - 2*x*(1+x)^2*A(x)^3 - 2^2*x^2*(1-x)*A(x)^4 + 2^3*x^3*A(x)^5.

Example

G.f.: A(x) = 1 + x + 7*x^2 + 27*x^3 + 165*x^4 + 877*x^5 + 5451*x^6 +...
where
log(A(x)) = (2*A(x) - 1)*x + (2*A(x) + 1)^2*x^2/2 + (2*A(x) - 1)^3*x^3/3 + (2*A(x) + 1)^4*x^4/4 +...
log(A(x)*(1-2*x*A(x))) = -1/(1 + 2*x*A(x))*x + 1/(1 - 2*x*A(x))^2*x^2/2 - 1/(1 + 2*x*A(x))^3*x^3/3 + 1/(1 - 2*x*A(x))^4*x^4/4 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (2*A+(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A185385, A163138, A202669, A155200.

Sequence in context: A179597 A295209 A151496 * A192250 A035081 A193257

Adjacent sequences: A202516 A202517 A202518 * A202520 A202521 A202522

Keyword

nonn

Author

Paul D. Hanna, Dec 22 2011

Status

approved