login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179470 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(2*x^n)*x^n/n ). 0
1, 1, 3, 15, 138, 2370, 78532, 5110472, 659436845, 169486506217, 86947958127377, 89122003350193045, 182611160539104099261, 748158103862060509908713, 6129659711065116858192667033, 100434475863953990317790200253757 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the g.f. of A000081: G(x) = exp( Sum_{n>=1} G(x^n)*x^n/n ).

LINKS

Table of n, a(n) for n=0..15.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 138*x^4 + 2370*x^5 +...

log(A(x)) = A(2x)*x + A(2x^2)*x^2/2 + A(2x^3)*x^3/3 + A(2x^4)*x^4/4 + A(2x^5)*x^5/5 +...

More generally, if F(x,q) = exp( Sum_{n>=1} F(q*x^n,q)*x^n/n )

then coefficients in F(x,q) = Sum_{n>=0} c(n,q)*x^n begin:

c(0,q) = 1; c(1,q) = 1; c(2,q) = q + 1;

c(3,q) = q^3 + q^2 + q + 1;

c(4,q) = q^6 + q^5 + q^4 + 2*q^3 + 3/2*q^2 + 3/2*q + 1;

c(5,q) = q^10 + q^9 + q^8 + 2*q^7 + 5/2*q^6 + 5/2*q^5 + 3*q^4 + 3*q^3 + 3/2*q^2 + 3/2*q + 1; ...

where C(n,q) are integers for integer values of q.

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, 2*x^m+x*O(x^n))*x^m/m))); polcoeff(A, n)}

CROSSREFS

Cf. A000081.

Sequence in context: A262911 A163949 A005816 * A270524 A179471 A203417

Adjacent sequences:  A179467 A179468 A179469 * A179471 A179472 A179473

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 15 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 13:31 EDT 2021. Contains 348042 sequences. (Running on oeis4.)