0,2

A transform of 3^n under the mapping g(x)->(1/sqrt(1-4x))g(xc(x)^2), where c(x) is the g.f. of the Catalan numbers A000108. A transform of 4^n under the mapping g(x)->(1/(c(x)sqrt(1-4x))g(xc(x)).

Hankel transform is A127357. In general, the Hankel transform of sum{k=0..n, C(2n,k)r^(n-k)} is the sequence with g.f. 1/(1-2x+r^2*x^2). - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007

G.f.: (sqrt(1-4x)+1)/(sqrt(1-4x)(4sqrt(1-4x)-2)); G.f.: sqrt(1-4x)(3sqrt(1-4x)-8x+3)/((1-4x)(6-32x)); a(n)=sum{k=0..n, binomial(2n, n-k)3^k}; a(n)=sum{k=0..n, binomial(2n, n-k)*sum{j=0..n, binomial(n, j)(-1)^(n-j)4^j}}.

a(n)=sum{k=0..n, C(2n,k)3^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007

a(n)=sum{k=0..n, C(n+k-1,k)4^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007

Cf. A032443, A100192.

Sequence in context: A052225 A015535 A026292 this_sequence A134425 A083326 A083880

Adjacent sequences: A100190 A100191 A100192 this_sequence A100194 A100195 A100196

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Nov 08 2004