OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973).
G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973). (Annotated scanned copy)
S.-n. Zheng and S.-l. Yang, On the-Shifted Central Coefficients of Riordan Matrices, Journal of Applied Mathematics, Volume 2014, Article ID 848374, 8 pages.
FORMULA
3-fold convolution of the large Schroeder numbers (A006318). G.f.: R^3, where R = [1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of A006318. - Emeric Deutsch, Mar 15 2004
a(n) = (3/n)*sum(binomial(n, j)*binomial(n+2+j, n-1), j=0..n) (n>0). - Emeric Deutsch, Aug 19 2004
Recurrence: (n+3)*(5*n-1)*a(n) = 2*(15*n^2+20*n+13)*a(n-1) - (5*n^2+5*n-24)*a(n-2) + (n-3)*a(n-3). - Vaclav Kotesovec, Oct 05 2012
a(n) ~ 3 * (1 + sqrt(2))^(2*n+3) / (2^(3/4) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Oct 05 2012, simplified Dec 24 2017
MAPLE
1, seq(3*sum(binomial(n, j)*binomial(n+2+j, n-1), j=0..n)/n, n=1..18);
MATHEMATICA
Table[SeriesCoefficient[(1-x-Sqrt[1-6*x+x^2])^3/(8*x^3), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 05 2012 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved