1,1

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

Next term has 180 digits and is too large to include. - 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.

a(n) is an element in the intersection of A001003 (super-Catalan numbers) and A001358 (semiprimes).

a(n) = A001003(A101618(n)). - David Wasserman (dwasserm(AT)earthlink.net), Mar 27 2008

a(1) = 4279 because it is super-Catalan and semiprime, since 4279 = 11 x 389.

a(2) = 2646723 because it is super-Catalan and 2646723 = 3 x 882241.

Similarly:

a(3) = 55909013009 = 41263 x 1354943.

a(4) = 1618362158587 = 24413 x 66290999.

a(5) = 47574827600981 = 3253 x 14624908577.

Cf. A001003, A001358.

Indices of Semiprime super-Catalan numbers: A101618. Indices of prime super-Catalan numbers: A092839. Prime super-Catalan numbers : A092840.

Sequence in context: A031985 A138399 A023346 this_sequence A124596 A165067 A055153

Adjacent sequences: A101616 A101617 A101618 this_sequence A101620 A101621 A101622

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 09 2004

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