A133444 a(n)=sum{k=0..n, C(n,floor(k/2))*(-1)^k*4^(n-k)}.

1, 3, 14, 57, 246, 1038, 4424, 18777, 79846, 339258, 1442004, 6128202, 26045436, 110691948, 470442924, 1999378137, 8497365126, 36113785698, 153483619604, 652305322542, 2772297736276, 11782265148228, 50074627320864, 212817165231882, 904472953925596

Offset: 0

Author

Philippe Deléham, Nov 26 2007

Keywords

• nonn

Comments

Hankel transform is 5^n . Second binomial transform is A076036 .

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Mathematica

Table[Sum[Binomial[n,Floor[k/2]]*(-1)^k*4^(n-k),{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 20 2012 *)

Formula

a(n)=Sum{k, 0<=k<=n} A053121(n,k)*A015521(k+1) = (-1)^n*A127363(n) . G.f.: (1/sqrt(1-4x^2))(1-xc(x^2))/(1-4x*c(x^2)), where c(x) is the g.f. of Catalan numbers A000108 .

Recurrence: 4*n*a(n) = (17*n-8)*a(n-1) + 2*(8*n+1)*a(n-2) - 68*(n-2)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 3*17^n/4^(n+1) . - Vaclav Kotesovec, Oct 20 2012

Extensions

More terms from Vincenzo Librandi, May 25 2013