login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157313 G.f.: exp( Sum_{n>=1} a(n)*x^n/n ) = Product_{n>=1} 1/(1 - a(n-1)*x^n). 1
1, 1, 3, 10, 43, 216, 1326, 9283, 74667, 672085, 6730098, 74031079, 888657130, 11552542691, 161747905609, 2426218982400, 38820193151115, 659943283568956, 11879029341157575, 225701557481993926, 4514035666639844778 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = Sum_{d divides n, 1<=d<=n} d * a(d-1)^(n/d) for n>0 with a(0)=1.

Product_{n>=1} 1/(1 - a(n-1)*x^n) = g.f. of A157314.

EXAMPLE

Define G(x) by the exponential:

G(x) = exp(x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 216*x^5/5 + 1326*x^6/6 +...)

then 1/G(x) also equals the product:

1/G(x) = (1 - x)(1 - x^2)(1 - 3*x^3)(1 - 10*x^4)(1 - 43*x^5)(1 - 216*x^6)*...

where the coefficients in both expressions are the same (with offset)

and G(x) is the g.f. of A157314:

G(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 62*x^5 + 298*x^6 + 1700*x^7 +...

PROG

(PARI) {a(n)=if(n==0, 1, sumdiv(n, d, if(d>=1&d<=n, d*(a(d-1))^(n/d))))}

(PARI) {a(n)=if(n==0, 1, n*polcoeff(1+sum(k=1, n, -log(1-a(k-1)*x^k +x*O(x^n))), n))}

(PARI) {a(n)=if(n==0, 1, n*polcoeff(sum(k=1, n, sum(j=1, n\k, a(k-1)^j*x^(k*j)/j)+x*O(x^n)), n))}

CROSSREFS

Cf. A157314, A157311.

Sequence in context: A030890 A030833 A318372 * A030971 A248687 A006932

Adjacent sequences:  A157310 A157311 A157312 * A157314 A157315 A157316

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 10 2009

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 May 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)