cp's OEIS Frontend

A104858 Partial sums of the little Schroeder numbers (A001003).

%I A104858 #28 Aug 05 2020 13:46:51
%S A104858 1,2,5,16,61,258,1161,5440,26233,129282,648141,3294864,16943733,
%T A104858 87983106,460676625,2429478144,12893056497,68802069506,368961496469,
%U A104858 1987323655056,10746633315501,58321460916482,317537398625945
%N A104858 Partial sums of the little Schroeder numbers (A001003).
%C A104858 The subsequence of primes begins: 2, 5, 61, no more through a(30). [_Jonathan Vos Post_, Feb 12 2010]
%H A104858 Vincenzo Librandi, <a href="/A104858/b104858.txt">Table of n, a(n) for n = 0..200</a>
%H A104858 Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a>, 2011. [Cached copy]
%H A104858 Guo-Niu Han, <a href="https://arxiv.org/abs/2006.14070">Enumeration of Standard Puzzles</a>, arXiv:2006.14070 [math.CO], 2020.
%F A104858 G.f.: (1 + z- sqrt(1 - 6*z + z^2))/(4*z*(1 - z)).
%F A104858 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
%F A104858 a(n) ~ sqrt(24 + 17*sqrt(2))*(3 + 2*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 17 2012
%F A104858 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
%p A104858 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);
%t A104858 CoefficientList[Series[(1+x-Sqrt[1-6*x+x^2])/4/x/(1-x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%Y A104858 Cf. A001003, A005408, A059993.
%K A104858 nonn
%O A104858 0,2
%A A104858 _Emeric Deutsch_, Apr 24 2005