A226908 L.g.f. L(x) = Sum_{n>=1} a(n)*x^n/n satisfies: exp(L(x)) = 1 + x*exp( Sum_{n>=1} a(n)*exp(L(x^n))*x^n/n ).

1, 1, 4, 9, 26, 64, 183, 465, 1282, 3406, 9285, 25044, 68511, 186565, 511559, 1402689, 3858355, 10623592, 29311035, 80957054, 223924131, 619998655, 1718508780, 4767643956, 13238487101, 36788341279, 102306350929, 284699560049, 792766449887, 2208805757329, 6157550533161

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

Logarithmic derivative of A226907.

Example

G.f.: L(x) = x + x^2/2 + 4*x^3/3 + 9*x^4/4 + 26*x^5/5 + 64*x^6/6 +...
where G(x) = exp(L(x)) satisfies
G(x) = 1 + x*exp( x*G(x) + x^2*G(x^2)/2 + 4*x^3*G(x^3)/3 + 9*x^4*G(x^4)/4 + 26*x^5*G(x^5)/5 + 64*x^6*G(x^6)/6 +...+ a(n)*x^n*G(x^n)/n +... )
and equals the g.f. of A226907:
G(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 20*x^6 + 48*x^7 + 113*x^8 + 276*x^9 + 677*x^10 +...+ A226907(n)*x^n +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*exp(sum(m=1, n, polcoeff(log(A+x*O(x^m)), m)*subst(A, x, x^m)*x^m)+x*O(x^n))); n*polcoeff(log(A), n)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A226907.

Sequence in context: A329125 A020181 A216134 * A328657 A335983 A113682

Adjacent sequences: A226905 A226906 A226907 * A226909 A226910 A226911

Keyword

nonn

Author

Paul D. Hanna, Jun 21 2013

Status

approved