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A120304
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Catalan number minus 2, or ((2n)!/n!/(n+1)! - 2).
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0
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-1, -1, 0, 3, 12, 40, 130, 427, 1428, 4860, 16794, 58784, 208010, 742898, 2674438, 9694843, 35357668, 129644788, 477638698, 1767263188, 6564120418, 24466267018, 91482563638, 343059613648, 1289904147322, 4861946401450, 18367353072150, 69533550916002, 263747951750358
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Prime p divides a(p). Prime p divides a(p+1) for p>2. Prime p divides a(p-1)/2) for p=13,17,29,37,41,53,61,73,89,97,101,109,113..=A002144[n] except 5. Pythagorean primes: primes of form 4n+1. Also A002313[n] except 2,5. Primes congruent to 1 or 2 modulo 4; or, primes of form x^2+y^2; or, -1 is a square mod p. p^2 divides a(p^2) and a(p^2+1) for all prime p.
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REFERENCES
| J.-L. Baril, Classical sequences revisited with permutations avoiding dotted pattern, Electronic Journal of Combinatorics, 18 (2011), #P178; http://www.combinatorics.org/Volume_18/PDF/v18i1p178.pdf.
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FORMULA
| a(n) = (2n)!/n!/(n+1)! - 2. a(n) = A000108[n] - 2.
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MAPLE
| (Mupad) combinat::dyckWords::count(n)-2 $ n = 0..38; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
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MATHEMATICA
| Table[(2n)!/n!/(n+1)!-2, {n, 0, 30}]
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CROSSREFS
| Cf. A000108, A002144, A002313, A003655.
Sequence in context: A080929 A061136 A027991 * A026071 A102839 A050182
Adjacent sequences: A120301 A120302 A120303 * A120305 A120306 A120307
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KEYWORD
| sign
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 13 2006
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