1,2

Reversion of g.f. for squares (ignoring signs).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

C. Domb and A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358 (column sums in Table 2).

P. Flajolet and M. Noy, Analytic Combinatorics of Non-crossing Configurations, Discrete Math. 204 (1999), 203-229.

T. D. Noe, Table of n, a(n) for n=1..100

F. Cazals, Combinatorics of Non-Crossing Configurations, Studies in Automatic Combinatorics, Volume II (1997).

E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.

P. Flajolet and M. Noy, Analytic Combinatorics of Non-crossing Configurations

Index entries for reversions of series

Sen-Peng Eu, Shu-Chung Liu and Yeong-Nan Yeh, On the congruences of some combinatorial numbers, Stud. Appl. Math. vol. 116 (2006) pp. 135-144

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 486

REVERT(A000290).

G.f.: (g-z)/z, where g=-1/3+(2/3)*sqrt(1+9z)*sin((1/3)*arcsin((2+27z+54z^2)/2/(1+9*z)^(3/2))); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 02 2002

a(n)=(1/n)*sum{k=0..n, binomial(3n, n-k-1)*binomial(n+k-1, k)}; - Paul Barry (pbarry(AT)wit.ie), May 11 2005

(Maple notation) an := 4^n*(GAMMA((3*n+1)/2)/GAMMA((n+3)/2)/GAMMA(n+1) -GAMMA( 3*n/2+1 )/GAMMA( n/2 +1)/GAMMA(n+2)); - Mark van Hoeij (Florida State Univ.), Aug 27 2005

C := binomial; an := 4^(n+1) * C(3*(n+1)/2, (n+1)/2) / (9*n+3) - 4^n * C(3*n/2, n/2 ) / (n+1); - Mark van Hoeij (Florida State Univ.), Aug 27 2005

-12*(3*n+2)*(3*n+1)*(3*n+8)*a(n)+(72+36*n)*a(n+1)+(3*n+5)*(n+3)*(n+2)*a(n+2) = 0 - Mark van Hoeij (Florida State Univ.), Aug 27 2005

a(n)=(1/n)*sum{k=0..n, C(3n, k)C(2n-k-2, n-1)}; - Paul Barry (pbarry(AT)wit.ie), Sep 27 2005

add(binomial(3*n - 3, n + j)*binomial(j - 1, j - n + 1), j = n - 1 .. 2*n - 3)/(n - 1);

(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-x^2)/(1+x)^3+O(x^(n+2))), n+1)) (from R. Stephan)

Sequence in context: A116881 A107089 A055723 this_sequence A111547 A158884 A053525

Adjacent sequences: A007294 A007295 A007296 this_sequence A007298 A007299 A007300

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)

Better description from Philippe Flajolet (Philippe.Flajolet(AT)inria.fr), Apr 20 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000