VOOZH about

URL: https://oeis.org/A104858

⇱ A104858 - OEIS

login
A104858
Partial sums of the little Schroeder numbers (A001003).
5
1, 2, 5, 16, 61, 258, 1161, 5440, 26233, 129282, 648141, 3294864, 16943733, 87983106, 460676625, 2429478144, 12893056497, 68802069506, 368961496469, 1987323655056, 10746633315501, 58321460916482, 317537398625945
OFFSET
0,2
COMMENTS
The subsequence of primes begins: 2, 5, 61, no more through a(30). [Jonathan Vos Post, Feb 12 2010]
LINKS
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
FORMULA
G.f.: (1 + z- sqrt(1 - 6*z + z^2))/(4*z*(1 - z)).
Recurrence: (n+1)*a(n) = (7*n-2)*a(n-1) - (7*n-5)*a(n-2) + (n-2)*a(n-3). - Vaclav Kotesovec, Oct 17 2012
a(n) ~ sqrt(24 + 17*sqrt(2))*(3 + 2*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 17 2012
Define a triangle T(n,1) = T(n,n) = 1 for n >= 1 and all other elements by T(r,c) = T(r,c-1) + T(r-1,c-1) + T(r-1,c). Its second column is A005408, its third column is A059993, and the sum of all terms in its row n is a(n-1). - J. M. Bergot, Dec 01 2012
MAPLE
G:=(1+z-sqrt(1-6*z+z^2))/4/z/(1-z): Gser:=series(G, z=0, 29): 1, seq(coeff(Gser, z^n), n=1..27);
MATHEMATICA
CoefficientList[Series[(1+x-Sqrt[1-6*x+x^2])/4/x/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 24 2005
STATUS
approved