login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192891 Expansion of g.f.: exp( Sum_{n>=1} 3^n*(Sum_{d|n} d*x^d)^n/n ). 3
1, 3, 9, 45, 153, 702, 2754, 11259, 50058, 224046, 990873, 4304988, 18175185, 77439321, 327135510, 1408297995, 6302244447, 29140976502, 135628856406, 622855827801, 2796140431278, 12364271615628, 54378167114070, 240937280782164, 1080881256295566 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

EXAMPLE

G.f.: A(x) = 1 + 3*x + 9*x^2 + 45*x^3 + 153*x^4 + 702*x^5 + 2754*x^6 + 11259*x^7 +...

where the logarithm of the g.f. begins:

log(A(x)) = 3*x + 9*(x + 2*x^2)^2/2 + 27*(x + 3*x^3)^3/3 + 81*(x + 2*x^2 + 4*x^4)^4/4 + 243*(x + 5*x^5)^5/5 + 729*(x + 2*x^2 + 3*x^3 + 6*x^6)^6/6 + 2187*(x + 7*x^7)^7/7 + 6561*(x + 2*x^2 + 4*x^4 + 8*x^8)^8/8 +...

Explicitly, the logarithmic series begins:

log(A(x)) = 3*x + 9*x^2/2 + 81*x^3/3 + 153*x^4/4 + 1458*x^5/5 + 3645*x^6/6 + 20898*x^7/7 + 100521*x^8/8 + 557685*x^9/9 + 2353374*x^10/10 +...

MATHEMATICA

With[{m = 40}, CoefficientList[Series[Exp[Sum[3^n (Sum[d*x^d, {d, Divisors[n]}])^n/n, {n, 1, m + 2}]], {x, 0, m}], x]] (* G. C. Greubel, Jan 10 2019 *)

PROG

(PARI) {a(n)=local(A); A=exp(sum(m=1, n+1, 3^m*sumdiv(m, d, d*x^d +x*O(x^n))^m/m)); polcoeff(A, n)}

CROSSREFS

Cf. A192860, A192890.

Sequence in context: A001902 A224085 A352797 * A068100 A327648 A262129

Adjacent sequences: A192888 A192889 A192890 * A192892 A192893 A192894

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 11 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:02 EST 2022. Contains 358656 sequences. (Running on oeis4.)