0,2

The convolution square root of this sequence is A004981. - T. D. Noe (noe(AT)sspectra.com), Jun 11 2002

Also main diagonal of array : T(i,1)=2^(i-1) T(1,j)=1 T(i,j)=T(i,j-1)+2*T(i-1,j). - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 26 2003

The Hankel transform (see A001906 for definition) of this sequence with interpolated zeros(1, 0, 4, 0, 24, 0, 160, 0, 1120, ...) = is A036442 : 1, 4, 32, 512, 16384, ... . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 03 2005

The Hankel transform of this sequence gives A103488 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2007

Equals the central column of the triangle A038207. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 08 2007

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

a(n) =a(n-1)*(8-4/n) =A000079(n)*A000984(n)

G.f.: A(x)=(1 - 8*x)^(-1/2) - T. D. Noe (noe(AT)sspectra.com), Jun 11 2002

E.g.f.: exp(4*x)*BesselI(0, 4*x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 20 2003

seq(binomial(2*n, n)*2^n, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 08 2007

(PARI) {a(n)=if(n<0, 0, 2^n*(2*n)!/n!^2)} /* Michael Somos Jan 31 2007 */

Diagonal of A013609.

Cf. A038207.

Adjacent sequences: A059301 A059302 A059303 this_sequence A059305 A059306 A059307

Sequence in context: A078108 A117337 A084130 this_sequence A069722 A027079 A052685

nonn

Henry Bottomley (se16(AT)btinternet.com), Jan 25 2001