A085458 a(n) = 4*Sum_{i=0..n-1} C(2*i+1, i)*C(n-1, n-1-i)*(-1)^(n-1-i)*2^i for n > 0, a(0) = 1.

1, 4, 20, 116, 708, 4452, 28532, 185300, 1215268, 8030404, 53381844, 356577588, 2391430020, 16092704292, 108605848116, 734783381652, 4982063186916, 33844621986180, 230306722637204, 1569571734301172, 10711405584991300

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Jul 02 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Andrei Asinowski, Cyril Banderier and Benjamin Hackl, Flip-sort and combinatorial aspects of pop-stack sorting, arXiv:2003.04912 [math.CO], 2020-2021; Discrete Mathematics & Theoretical Computer Science, April 30, 2021, vol. 22 no. 2. Formula 25.

Crossrefs

Cf. A085456 (signed version).

Programs

Mathematica

CoefficientList[Series[Sqrt[(1 + x)/(1 - 7x)], {x, 0, 25}], x]

PARI

x='x+O('x^66); Vec(sqrt((1+x)/(1-7*x))) \\ Joerg Arndt, May 10 2013

Formula

G.f.: sqrt((1 + x)/(1 - 7*x)).

7^n = Sum_{i=0..n} Sum_{j=0..i} (-1)^(n-i)*a(j)*a(i-j).

Recurrence: n*a(n) = 2*(3*n-1)*a(n-1) + 7*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ 2*sqrt(2)*7^(n-1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 14 2012