A304637 G.f. A(x) satisfies: A(x) = 1 + x*Sum_{n>=0} (A(x)^n - 1/A(x)^n)^n.

1, 1, 2, 19, 299, 6241, 160020, 4858616, 171069361, 6885389368, 313162056098, 15930678907603, 897891292501468, 55589209442827830, 3751221859059876602, 274034654053985700103, 21542764404180713248407, 1813058710831887654110832, 162622164570756746546500432, 15484376910535107858657060827, 1559723646248351386009584065673, 165693824812298090074580795882273

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 19*x^3 + 299*x^4 + 6241*x^5 + 160020*x^6 + 4858616*x^7 + 171069361*x^8 + 6885389368*x^9 + 313162056098*x^10 + ...
such that g.f. A = A(x) satisfies:
A(x) = 1 + x*(1 + (A - 1/A) + (A^2 - 1/A^2)^2 + (A^3 - 1/A^3)^3 + (A^4 - 1/A^4)^4 + (A^5 - 1/A^5)^5 + ...).
RELATED SERIES.
x/Series_Reversion(A(x) - 1) = 1 + 2*x + 15*x^2 + 201*x^3 + 3807*x^4 + 93103*x^5 + 2788528*x^6 + 98816388*x^7 + 4043274742*x^8 + 187583369889*x^9 + 9729671519992*x^10 + ...

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = 1 + x*sum(m=0, n, (A^m - 1/A^m +x*O(x^n))^m )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A293946 A365652 A094476 * A119773 A137647 A233107

Adjacent sequences: A304634 A304635 A304636 * A304638 A304639 A304640

Keyword

nonn

Author

Paul D. Hanna, May 15 2018

Status

approved