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 A050511 a(n) = (-1)^n * Sum_{i=0..n} binomial(n+1,i+1)*Catalan(i). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 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 MATHEMATICA Table[(-1)^n Sum[Binomial[n+1, i+1]CatalanNumber[i], {i, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Jan 26 2013 *) CROSSREFS Column 1 of A091698. Sequence in context: A047857 A101495 A134758 * A151405 A148778 A099265 Adjacent sequences:  A050508 A050509 A050510 * A050512 A050513 A050514 KEYWORD sign AUTHOR N. J. A. Sloane, Dec 28 1999 STATUS approved

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)