A226907 G.f. satisfies: A(x) = 1 + x*exp( Sum_{n>=1} A226908(n)*A(x^n)*x^n/n ), where A(x) = exp( Sum_{n>=1} A226908(n)*x^n/n ).

1, 1, 1, 2, 4, 9, 20, 48, 113, 276, 677, 1688, 4235, 10750, 27441, 70583, 182540, 474661, 1239813, 3252340, 8563354, 22625355, 59964165, 159379210, 424722489, 1134561965, 3037511482, 8149024111, 21904177974, 58982864413, 159092896924, 429789420025, 1162782671824, 3150222065843, 8545720220802

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 20*x^6 + 48*x^7 +...
where
A(x) = exp(x + x^2/2 + 4*x^3/3 + 9*x^4/4 + 26*x^5/5 + 64*x^6/6 + 183*x^7/7 + 465*x^8/8 + 1282*x^9/9 + 3406*x^10/10 +...+ A226908(n)*x^n/n +...)
such that
A(x) = 1 + x*exp(x*A(x) + x^2*A(x^2)/2 + 4*x^3*A(x^3)/3 + 9*x^4*A(x^4)/4 + 26*x^5*A(x^5)/5 + 64*x^6*A(x^6)/6 + 183*x^7*A(x^7)/7 + 465*x^8*A(x^8)/8 + 1282*x^9*A(x^9)/9 + 3406*x^10*A(x^10)/10  +...+ A226908(n)*x^n*A(x^n)/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))); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A226908, A000081.

Sequence in context: A052329 A199883 A036624 * A186952 A034823 A036625

Adjacent sequences: A226904 A226905 A226906 * A226908 A226909 A226910

Keyword

nonn

Author

Paul D. Hanna, Jun 21 2013

Status

approved