0,3

a(n)=(n+1)*A000984 n>=-1 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 18 2007

a(n+1) is the convolution of A000984 and A081294. [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2008]

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972.

a(n)=(n+1)*binomial(2*n,n), n>=-1 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 18 2007

Starting (1, 4, 18, 80,...), = binomial transform of A134757: (1, 3, 11, 37, 123, 401,...); and double binomial transform of A100071 starting (1, 2, 6, 12, 30,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 08 2007

G.f.: F(1/2,2;1;4x); [From Paul Barry (pbarry(AT)wit.ie), Sep 03 2008]

Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 18 2008: (Start)

G.f.: x(1-2x)/(1-4x)^(3/2);

a(n+1)=sum{k=0..n, C(2k,k)*(4^(n-k)+0^(n-k))/2}; (End)

seq((n+1)*binomial(2*n, n), n=-1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 18 2007

a:=n->add(binomial(2*n, n), k=0..n): seq(a(n), n=-1..21); - ZerinvaryLajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

with(combstruct):with(combinat) :bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, unlabeled], size=n)*n^2, n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 05 2007

Table[CatalanNumber[n]*(n + 1)^2, {n, -1, 21}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]

Cf. A000984.

Cf. A134757, A100071.

Sequence in context: A100069 A058870 A112619 this_sequence A045902 A090017 A104631

Adjacent sequences: A037962 A037963 A037964 this_sequence A037966 A037967 A037968

nonn

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

More terms from ZerinvaryLajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007