A202669 G.f. satisfies: A(x) = exp( Sum_{n>=1} (A(x) + (-1)^n)^n * x^n/n ).

1, 0, 2, 2, 12, 20, 96, 212, 898, 2354, 9266, 27070, 102094, 319930, 1177838, 3865762, 14050948, 47574460, 171886784, 594572676, 2143957648, 7528825924, 27156892364, 96412294088, 348314869652, 1246689890248, 4513958859208, 16257651642036, 59010423148052, 213586733348928

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Formula

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

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

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

Example

G.f.: A(x) = 1 + 2*x^2 + 2*x^3 + 12*x^4 + 20*x^5 + 96*x^6 + 212*x^7 +...
where
log(A(x)) = (A(x) - 1)*x + (A(x) + 1)^2*x^2/2 + (A(x) - 1)^3*x^3/3 + (A(x) + 1)^4*x^4/4 +...
log(A(x)*(1-x*A(x))) = -1/(1 + x*A(x))*x + 1/(1 - x*A(x))^2*x^2/2 - 1/(1 + x*A(x))^3*x^3/3 + 1/(1 - 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, (A+(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A202668, A202629, A202519, A155200.

Sequence in context: A194767 A302368 A346757 * A178845 A140431 A092900

Adjacent sequences: A202666 A202667 A202668 * A202670 A202671 A202672

Keyword

nonn

Author

Paul D. Hanna, Dec 22 2011

Status

approved