1,2

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

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.yu), 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,easy

njas

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