1,2

First column of triangle A100326. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 16 2004

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

M. Bicknell and V. E. Hoggatt, Jr., Sequences of matrix inverses from Pascal, Catalan and related convolution arrays, Fib. Quart., 14 (1976), 224-232.

L. Carlitz, Enumeration of two-line arrays, Fib. Quart., 11 (1973), 113-130.

R. C. Read, On the enumeration of a class of plane multigraphs, Aequat. Math., 31 (1986), 47-63.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 416

For formula see Read reference.

a(n) = ( (324*n^2-708*n+360)*a(n-1) - (371*n^2-1831*n+2250)*a(n-2) + (20*n^2-130*n+210)*a(n-3) )/(16*n*(2*n-1)) for n>2, with a(0)=0, a(1)=1, a(2)=3. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 16 2004

G.f. satisfies: A(x) = x*(1+A(x))/(1-A(x))^2 where A(0)=0. G.f. satisfies: (1+A(x))/(1-A(x)) = 2*G003168(x)-1, where G003168 is the g.f. of A003168. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 16 2004

a(n) = (1/n)*Sum_{i=0..n-1} binomial(n,i)*binomial(3*n-i-2,n-i-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 13 2006

a[0]:=0:a[1]:=1:a[2]:=3:for n from 3 to 30 do a[n]:=((324*n^2-708*n+360)*a[n-1] -(371*n^2-1831*n+2250)*a[n-2]+(20*n^2-130*n+210)*a[n-3])/(16*n*(2*n-1)) od:seq(a[n], n=1..25); (Deutsch)

(PARI) {a(n)=if(n==0, 0, if(n==1, 1, if(n==2, 3, ( (324*n^2-708*n+360)*a(n-1) -(371*n^2-1831*n+2250)*a(n-2)+(20*n^2-130*n+210)*a(n-3))/(16*n*(2*n-1)) )))} (Hanna)

(PARI) {a(n)=local(A=x+x*O(x^n)); if(n==1, 1, for(i=1, n, A=x*(1+A)/(1-A)^2); polcoeff(A, n))}

Cf. A003168, A100324, A100326.

Sequence in context: A074538 A001564 A059276 this_sequence A086621 A020089 A027614

Adjacent sequences: A003166 A003167 A003168 this_sequence A003170 A003171 A003172

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 31 2005