A202518
G.f. satisfies: A(x) = exp( Sum_{n>=1} (2^n - A(x))^n * x^n/n ).
Original entry on oeis.org
1, 1, 4, 111, 12600, 5722258, 10419647136, 76124127132667, 2234758718926030048, 263964471372716219981614, 125532541357451846737479404864, 240382906462440786858510574342553910, 1852958218856132372722626702327036659515008
Offset: 0
G.f.: A(x) = 1 + x + 4*x^2 + 111*x^3 + 12600*x^4 + 5722258*x^5 +...
where
log(A(x)) = (2 - A(x))*x + (2^2 - A(x))^2*x^2/2 + (2^3 - A(x))^3*x^3/3 + (2^4 - A(x))^4*x^4/4 +...
-
{a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,(2^m-A+x*O(x^n))^m*x^m/m)));polcoeff(A,n)}
A202519
G.f. satisfies: A(x) = exp( Sum_{n>=1} (2*A(x) + (-1)^n)^n * x^n/n ).
Original entry on oeis.org
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
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 +...
-
{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)}
A185385
G.f. satisfies: A(x) = exp( Sum_{n>=1} (2*A(x) - (-1)^n)^n * x^n/n ).
Original entry on oeis.org
1, 3, 11, 61, 381, 2527, 17559, 126265, 931321, 7007035, 53568131, 414929621, 3249392917, 25684315319, 204645707183, 1641910625009, 13253684541553, 107561523423731, 877109999610107, 7183095973808493, 59053492869471661, 487189276030904207, 4032100262853037127
Offset: 0
G.f.: A(x) = 1 + 3*x + 11*x^2 + 61*x^3 + 381*x^4 + 2527*x^5 + 17559*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 +...
-
{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)}
Showing 1-3 of 3 results.
Comments