1,3

A Catalan transform of A078008 under the mapping g(x)->g(xc(x)). - Paul Barry (pbarry(AT)wit.ie), Nov 13 2004

a(n) = A108561(2*(n-1),n-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2005

Number of positive terms in expansion of (x_1+x_2+...+x_{n-1}-x_n)^n. - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Feb 08 2007

Hankel transform is A088138(n+1). [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]

Without the beginning "1", we obtain the first diagonal over the principal diagonal of the array notified by B. Cloitre in A026641 and used by R. Choulet in A172025, and from A172061 to A172066 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 25 2010]

Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.

If offset is 0, a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n+k-1, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2003

G.f.: x*(1-x*C)/(1-2*x*C)/(1+x*C), where C = (1-(1-4*x)^(1/2))/x/2 is g.f. for Catalan numbers (A000108). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2003

a(n)=sum(binomial(2n-2j-4, n-3), j=0..floor((n-1)/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 28 2004

a(n)=(-1)^n*sum{k=0..n, C(-n,k)} (offset 0). [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]

Other form of the G.f: f(z)=(2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^(-1). [From Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 25 2010]

The array begins:

1 0 1 0 1..

0 0 1 1 2..

1 1 2 3 5..

0 1 3 6 11..

taylor( (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^(-1), z=0, 42); for n from -1 to 40 do a(n):=sum('(-1)^(p)*binomial(2n-p+1, 1+n-p)', p=0..n+1): od:seq(a(n), n=-1..40):od; [From Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 25 2010]

Cf. A014300, A026641, A092785.

Sequence in context: A148496 A106434 A150228 this_sequence A150229 A150230 A150231

A026641, A172025, from A172061 to A172066 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 25 2010]

Adjacent sequences: A072544 A072545 A072546 this_sequence A072548 A072549 A072550

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2002

Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 17 2003