A233336 E.g.f. A(x) satisfies: A( Integral 1/A(x)^2 dx ) = exp(x).

1, 1, 3, 19, 201, 3097, 63963, 1677883, 53862225, 2059533745, 91909156083, 4711414480867, 273922577628057, 17876478783834313, 1298278981158825291, 104165674946626478347, 9175884838706696138145, 882669439812976183138657, 92284482487864563215652579, 10443186091555501868233274803

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f. satisfies: A(x) = exp( Series_Reversion( Integral 1/A(x)^2 dx ) ).

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 201*x^4/4! + 3097*x^5/5! + 63963*x^6/6! +...
Related expansions.
A(x)^2 = 1 + 2*x + 8*x^2/2! + 56*x^3/3! + 608*x^4/4! + 9344*x^5/5! + 190400*x^6/6! +...+ A233335(n)*(2*x)^n/n! +...
Integral 1/A(x)^2 dx = x - 2*x^2/2! - 8*x^4/4! - 96*x^5/5! - 1664*x^6/6! +...
The series reversion of the Integral 1/A(x)^2 dx equals log(A(x)) and begins:
log(A(x)) = x + 2*x^2/2! + 12*x^3/3! + 128*x^4/4! + 2016*x^5/5! + 42656*x^6/6! + 1145280*x^7/7! + 37563008*x^8/8! +...+ A259267(n)*x^n/n! +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(serreverse(intformal(1/A^2+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A233335, A259267.

Sequence in context: A127502 A175176 A362968 * A208897 A027546 A301419

Adjacent sequences: A233333 A233334 A233335 * A233337 A233338 A233339

Keyword

nonn

Author

Paul D. Hanna, Dec 07 2013

Status

approved