A050511 a(n) = (-1)^n * Sum_{i=0..n} binomial(n+1,i+1)*Catalan(i).

1, -3, 8, -23, 74, -262, 993, -3943, 16178, -68000, 291191, -1265618, 5568263, -24749363, 110961248, -501209303, 2278704938, -10419244888, 47882934663, -221047167628, 1024586641973, -4766517165713, 22248226873538, -104160733650738, 489007907489239

Offset: 0

Author

N. J. A. Sloane, Dec 28 1999

Keywords

• sign

References

• J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 371.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Column 1 of A091698.

Programs

Mathematica

Table[(-1)^n Sum[Binomial[n+1,i+1]CatalanNumber[i],{i,0,n}],{n,0,30}] (* Harvey P. Dale, Jan 26 2013 *)

Formula

G.f.: (sqrt((5*x+1)/(x+1))-1)/(2*x*(x+1)).

(n+1)*a(n)=(1-6*n)*a(n-1)-5*n*a(n-2)+(-1)^n. - Vladeta Jovovic, Jul 16 2004

a(n) ~ (-1)^n * 5^(n+5/2) / (32 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 02 2014