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!)
A307398 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 - x^k). 2
1, 1, 4, 13, 52, 209, 906, 4010, 18303, 85064, 402008, 1924412, 9314594, 45502924, 224068334, 1111017056, 5542331502, 27796367468, 140072333426, 708875098462, 3601278993411, 18359296689521, 93892611212526, 481575492271765, 2476572824391335, 12767331527712854 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k * Sum_{d|k} d*A(x)^d.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 52*x^4 + 209*x^5 + 906*x^6 + 4010*x^7 + 18303*x^8 + 85064*x^9 + 402008*x^10 + ...

MATHEMATICA

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x]^k/(1 - x^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[x^k Sum[d A[x]^d, {d, Divisors[k]}], {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

CROSSREFS

Cf. A000203, A192207, A307396, A307400.

Sequence in context: A149463 A323791 A149464 * A129147 A151476 A140454

Adjacent sequences:  A307395 A307396 A307397 * A307399 A307400 A307401

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 07 2019

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 6 23:46 EDT 2021. Contains 343603 sequences. (Running on oeis4.)