1,1

Super-Catalan numbers are also known as little Schroeder numbers.

No more terms < 2000. - David Wasserman (dwasserm(AT)earthlink.net), Mar 27 2008

Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 56, 1974.

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Exercise 7.50 in Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.

Motzkin, T. "Relations Between Hypersurface Cross Ratios and a Combinatorial Formula for Partitions of a Polygon for Permanent Preponderance and for Non-Associative Products." Bull. Amer. Math. Soc. 54, 352-360, 1948.

Eric Weisstein's World of Mathematics, Super Catalan Number.

Eric Weisstein's World of Mathematics, Semiprime.

A001003(a(n)) is in A001358 (semiprimes).

a(1) = 7 because because super-Catalan(7) = 4279 = 11 x 389.

a(2) = 11 because super-Catalan(11) = 2646723 = 3 x 882241.

a(3) = 17 because super-Catalan(17) = 55909013009 = 41263 x 1354943.

a(4) = 19 because super-Catalan(19) = 1618362158587 = 24413 x 66290999.

a(5) = 21 because super-Catalan(21) = 47574827600981 = 3253 x 14624908577.

Cf. A001003, A001358.

Semiprime super-Catalan numbers: A101619. Indices of prime super-Catalan numbers: A092839. Prime super-Catalan numbers: A092840.

Sequence in context: A131626 A086762 A076045 this_sequence A117743 A034849 A106070

Adjacent sequences: A101615 A101616 A101617 this_sequence A101619 A101620 A101621

nonn,more

Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 09 2004

Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 07 2006

Changed by Michael Somos, Mar 31 2007, because of the re-indexing of A001003.

a(6) from David Wasserman (dwasserm(AT)earthlink.net), Mar 27 2008