A048286 Eigensequence of a sequence transformation.

1, 2, 10, 80, 874, 12092, 202384, 3973580, 89515690, 2275453700, 64418414380, 2009835207800, 68512342137040, 2533368817192280, 100991942945221660, 4317627768285138020, 197054129197204173610, 9562339765515442736180

Offset

0,2

Comments

G.f. A(x) satisfies A(x)=(A(0)+A(x/(1-x)^2)(1+x)/(1-x))/2.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Octavio Arizmendi, Takahiro Hasebe, and Franz Lehner, Cyclic independence: Boolean and monotone, arXiv:2204.00072 [math.PR], 2022.

C. J. Smyth, The mean values of algebraic integers, Math. Comp 42 (1984), 663-681; see eqs. (5.4), (5.8), (5.12).

Formula

a(n) ~ c * 2^n * n^(n + 1/2 - log(2)/4) / (exp(n) * (log(2))^n), where c = 1.64631699329139900560839601704146775549945357007201882... . - Vaclav Kotesovec, Aug 08 2014

Prog

(PARI) a(n)=local(A); if(n<1, n==0, A=1; for(k=1, n, A=1+Pol(subst(A+x*O(x^k), x, x/(1-x)^2)*(1+x)/(1-x))-A); polcoeff(A, n))

Crossrefs

Sequence in context: A371460 A220112 A367851 * A227463 A008544 A133480

Adjacent sequences: A048283 A048284 A048285 * A048287 A048288 A048289

Keyword

nonn

Author

Christopher J. Smyth

Extensions

Edited by Michael Somos, Sep 24 2003

Status

approved